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\documentclass[12pt,a4paper]{article}
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\usepackage{amssymb}
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\begin{document}
\begin{enumerate}[\quad 1)]
\item $y =  (x-5)\cdot \sqrt{x^2+7 x+10}$, \quad $y'=\dfrac{4 x^2+11 x-15}{2  \sqrt{x^2+7 x+10}}$. \hfill Answer. $x=1.$ \item $y = (x-4)\cdot \sqrt{x^2+6 x+5}$, \quad $y'=\dfrac{2 x^2+5 x-7}{\sqrt{x^2+6 x+5}}$. \hfill  Answer. $x=1.$ \item $y = (x-1)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{2 x^2-25 x+68}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=4.$ \item $y = (x+1)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{2 x^2-17 x+26}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (x+1)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{4 x^2-43 x+93}{2 \sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (x+2)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{2 x^2-13 x+11}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=1.$ \item $y = (x+2)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{4 x^2-35 x+54}{2 \sqrt{x^2-13 x+40}}$. \hfill Answer. $x=2.$ \item $y = (x+3)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{x (2 x-9)}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=0.$ \item $y = (x+3)\cdot \sqrt{x^2-11 x+28}$, \quad $y'=\dfrac{4 x^2-27 x+23}{2 \sqrt{x^2-11 x+28}}$. \hfill Answer. $x=1.$ \item $y = (x+4)\cdot \sqrt{x^2-6 x+5}$, \quad $y'=\dfrac{2 x^2-5 x-7}{\sqrt{x^2-6 x+5}}$. \hfill Answer. $x=-1.$ \item $y = (x+4)\cdot \sqrt{x^2-9 x+18}$, \quad $y'=\dfrac{x (4 x-19)}{2 \sqrt{x^2-9 x+18}}$. \hfill Answer. $x=0.$ \item $y = (x+5)\cdot \sqrt{x^2-7 x+10}$, \quad $y'=\dfrac{4 x^2-11 x-15}{2 \sqrt{x^2-7 x+10}}$. \hfill Answer. $x=-1.$ \item $y = (x+6)\cdot \sqrt{x^2-2 x-3}$, \quad $y'=\dfrac{2 x^2+3 x-9}{\sqrt{x^2-2 x-3}}$. \hfill Answer. $x=-3.$ \item $y = (x+6)\cdot \sqrt{x^2-5 x+4}$, \quad $y'=\dfrac{4 x^2-3 x-22}{2 \sqrt{x^2-5 x+4}}$. \hfill Answer. $x=-2.$ \item $y = (x+7)\cdot \sqrt{x^2-4}$, \quad $y'=\dfrac{2 x^2+7 x-4}{\sqrt{x^2-4}}$. \hfill Answer. $x=-4.$ \item $y = (x+8)\cdot \sqrt{x^2+2 x-3}$, \quad $y'=\dfrac{2 x^2+11 x+5}{\sqrt{x^2+2 x-3}}$. \hfill Answer. $x=-5.$ \item $y = (x+8)\cdot \sqrt{x^2-x-2}$, \quad $y'=\dfrac{4 x^2+13 x-12}{2 \sqrt{x^2-x-2}}$. \hfill Answer. $x=-4.$ \item $y = (x+8)\cdot \sqrt{x^2-12 x+20}$, \quad $y'=\dfrac{2 \left(x^2-5 x-14\right)}{\sqrt{x^2-12 x+20}}$. \hfill Answer. $x=-2.$ \item $y = (x+9)\cdot \sqrt{x^2+x-2}$, \quad $y'=\dfrac{4 x^2+21 x+5}{2 \sqrt{x^2+x-2}}$. \hfill Answer. $x=-5.$ \item $y = (x+9)\cdot \sqrt{x^2-10 x+9}$, \quad $y'=\dfrac{2 \left(x^2-3 x-18\right)}{\sqrt{x^2-10 x+9}}$. \hfill Answer. $x=-3.$ \item $y = (x+10)\cdot \sqrt{x^2+6 x+5}$, \quad $y'=\dfrac{2 x^2+19 x+35}{\sqrt{x^2+6 x+5}}$. \hfill Answer. $x=-7.$ \item $y = (x+10)\cdot \sqrt{x^2-8 x-20}$, \quad $y'=\dfrac{2 \left(x^2-x-30\right)}{\sqrt{x^2-8 x-20}}$. \hfill Answer. $x=-5.$ \item $y = (x+10)\cdot \sqrt{x^2-14 x+40}$, \quad $y'=\dfrac{2 x^2-11 x-30}{\sqrt{x^2-14 x+40}}$. \hfill Answer. $x=-2.$ \item $y = (2 x-5)\cdot \sqrt{x^2-12 x+35}$, \quad $y'=\dfrac{4 x^2-41 x+100}{\sqrt{x^2-12 x+35}}$. \hfill Answer. $x=4.$ \item $y = (2 x-3)\cdot \sqrt{x^2+4 x+3}$, \quad $y'=\dfrac{x (4 x+9)}{\sqrt{x^2+4 x+3}}$. \hfill Answer. $x=0.$ \item $y = (2 x-3)\cdot \sqrt{x^2-10 x+24}$, \quad $y'=\dfrac{4 x^2-33 x+63}{\sqrt{x^2-10 x+24}}$. \hfill Answer. $x=3.$ \item $y = (2 x-2)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{2 \left(2 x^2-25 x+68\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=4.$ \item $y = (2 x-1)\cdot \sqrt{x^2+6 x+8}$, \quad $y'=\dfrac{4 x^2+17 x+13}{\sqrt{x^2+6 x+8}}$. \hfill Answer. $x=-1.$ \item $y = (2 x-1)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{4 x^2-25 x+34}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=2.$ \item $y = (2 x+1)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{4 x^2+25 x+34}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-2.$ \item $y = (2 x+1)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{4 x^2-17 x+13}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=1.$ \item $y = (2 x+2)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{4 x^2-34 x+52}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (2 x+2)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{4 x^2-43 x+93}{\sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (2 x+3)\cdot \sqrt{x^2-4 x+3}$, \quad $y'=\dfrac{x (4 x-9)}{\sqrt{x^2-4 x+3}}$. \hfill Answer. $x=0.$ \item $y = (2 x+4)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{4 x^2-26 x+22}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=1.$ \item $y = (2 x+4)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{4 x^2-35 x+54}{\sqrt{x^2-13 x+40}}$. \hfill Answer. $x=2.$ \item $y = (2 x+6)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{2 x (2 x-9)}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=0.$ \item $y = (2 x+6)\cdot \sqrt{x^2-11 x+28}$, \quad $y'=\dfrac{4 x^2-27 x+23}{\sqrt{x^2-11 x+28}}$. \hfill Answer. $x=1.$ \item $y = (2 x+7)\cdot \sqrt{x^2-1}$, \quad $y'=\dfrac{4 x^2+7 x-2}{\sqrt{x^2-1}}$. \hfill Answer. $x=-2.$ \item $y = (2 x+7)\cdot \sqrt{x^2-14 x+40}$, \quad $y'=\dfrac{4 x^2-35 x+31}{\sqrt{x^2-14 x+40}}$. \hfill Answer. $x=1.$ \item $y = (2 x+8)\cdot \sqrt{x^2-6 x+5}$, \quad $y'=\dfrac{2 \left(2 x^2-5 x-7\right)}{\sqrt{x^2-6 x+5}}$. \hfill Answer. $x=-1.$ \item $y = (2 x+8)\cdot \sqrt{x^2-9 x+18}$, \quad $y'=\dfrac{x (4 x-19)}{\sqrt{x^2-9 x+18}}$. \hfill Answer. $x=0.$ \item $y = (2 x+9)\cdot \sqrt{x^2-12 x+27}$, \quad $y'=\dfrac{x (4 x-27)}{\sqrt{x^2-12 x+27}}$. \hfill Answer. $x=0.$ \item $y = (2 x+10)\cdot \sqrt{x^2-7 x+10}$, \quad $y'=\dfrac{4 x^2-11 x-15}{\sqrt{x^2-7 x+10}}$. \hfill Answer. $x=-1.$ \item $y = (3 x-5)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{6 x^2+31 x+25}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-1.$ \item $y = (3 x-5)\cdot \sqrt{x^2+6 x+5}$, \quad $y'=\dfrac{2 x (3 x+11)}{\sqrt{x^2+6 x+5}}$. \hfill Answer. $x=0.$ \item $y = (3 x-5)\cdot \sqrt{x^2-9 x+20}$, \quad $y'=\dfrac{12 x^2-91 x+165}{2 \sqrt{x^2-9 x+20}}$. \hfill Answer. $x=3.$ \item $y = (3 x-4)\cdot \sqrt{x^2+3 x+2}$, \quad $y'=\dfrac{x (12 x+19)}{2 \sqrt{x^2+3 x+2}}$. \hfill Answer. $x=0.$ \item $y = (3 x-4)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{2 \left(3 x^2-29 x+60\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=3.$ \item $y = (3 x-4)\cdot \sqrt{x^2-14 x+48}$, \quad $y'=\dfrac{6 x^2-67 x+172}{\sqrt{x^2-14 x+48}}$. \hfill Answer. $x=4.$ \item $y = (3 x-3)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{3 \left(2 x^2-25 x+68\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=4.$ \item $y = (3 x-2)\cdot \sqrt{x^2-7 x+12}$, \quad $y'=\dfrac{12 x^2-67 x+86}{2 \sqrt{x^2-7 x+12}}$. \hfill Answer. $x=2.$ \item $y = (3 x-1)\cdot \sqrt{x^2+5 x+6}$, \quad $y'=\dfrac{12 x^2+43 x+31}{2 \sqrt{x^2+5 x+6}}$. \hfill Answer. $x=-1.$ \item $y = (3 x-1)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{6 x^2-46 x+68}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=2.$ \item $y = (3 x-1)\cdot \sqrt{x^2-12 x+35}$, \quad $y'=\dfrac{6 x^2-55 x+111}{\sqrt{x^2-12 x+35}}$. \hfill Answer. $x=3.$ \item $y = (3 x+1)\cdot \sqrt{x^2-5 x+6}$, \quad $y'=\dfrac{12 x^2-43 x+31}{2 \sqrt{x^2-5 x+6}}$. \hfill Answer. $x=1.$ \item $y = (3 x+2)\cdot \sqrt{x^2+7 x+12}$, \quad $y'=\dfrac{12 x^2+67 x+86}{2 \sqrt{x^2+7 x+12}}$. \hfill Answer. $x=-2.$ \item $y = (3 x+2)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{6 x^2-34 x+28}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=1.$ \item $y = (3 x+2)\cdot \sqrt{x^2-10 x+24}$, \quad $y'=\dfrac{6 x^2-43 x+62}{\sqrt{x^2-10 x+24}}$. \hfill Answer. $x=2.$ \item $y = (3 x+3)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{6 x^2-51 x+78}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (3 x+3)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{3 \left(4 x^2-43 x+93\right)}{2 \sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (3 x+4)\cdot \sqrt{x^2-3 x+2}$, \quad $y'=\dfrac{x (12 x-19)}{2 \sqrt{x^2-3 x+2}}$. \hfill Answer. $x=0.$ \item $y = (3 x+5)\cdot \sqrt{x^2+9 x+20}$, \quad $y'=\dfrac{12 x^2+91 x+165}{2 \sqrt{x^2+9 x+20}}$. \hfill Answer. $x=-3.$ \item $y = (3 x+5)\cdot \sqrt{x^2-6 x+5}$, \quad $y'=\dfrac{2 x (3 x-11)}{\sqrt{x^2-6 x+5}}$. \hfill Answer. $x=0.$ \item $y = (3 x+5)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{6 x^2-31 x+25}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=1.$ \item $y = (3 x+6)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{6 x^2-39 x+33}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=1.$ \item $y = (3 x+6)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{3 \left(4 x^2-35 x+54\right)}{2 \sqrt{x^2-13 x+40}}$. \hfill Answer. $x=2.$ \item $y = (3 x+8)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{x (6 x-19)}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=0.$ \item $y = (3 x+9)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{3 x (2 x-9)}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=0.$ \item $y = (3 x+9)\cdot \sqrt{x^2-11 x+28}$, \quad $y'=\dfrac{3 \left(4 x^2-27 x+23\right)}{2 \sqrt{x^2-11 x+28}}$. \hfill Answer. $x=1.$ \item $y = (3 x+10)\cdot \sqrt{x^2-12 x+20}$, \quad $y'=\dfrac{2 x (3 x-22)}{\sqrt{x^2-12 x+20}}$. \hfill Answer. $x=0.$ \item $y = (3 x+10)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{2 \left(3 x^2-31 x+50\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=2.$ \item $y = (4 x-5)\cdot \sqrt{x^2-14 x+40}$, \quad $y'=\dfrac{8 x^2-89 x+195}{\sqrt{x^2-14 x+40}}$. \hfill Answer. $x=3.$ \item $y = (4 x-5)\cdot \sqrt{x^2-18 x+80}$, \quad $y'=\dfrac{8 x^2-113 x+365}{\sqrt{x^2-18 x+80}}$. \hfill Answer. $x=5.$ \item $y = (4 x-4)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{4 \left(2 x^2-25 x+68\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=4.$ \item $y = (4 x-2)\cdot \sqrt{x^2+6 x+8}$, \quad $y'=\dfrac{8 x^2+34 x+26}{\sqrt{x^2+6 x+8}}$. \hfill Answer. $x=-1.$ \item $y = (4 x-2)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{8 x^2-50 x+68}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=2.$ \item $y = (4 x-1)\cdot \sqrt{x^2-12 x+27}$, \quad $y'=\dfrac{8 x^2-73 x+114}{\sqrt{x^2-12 x+27}}$. \hfill Answer. $x=2.$ \item $y = (4 x-1)\cdot \sqrt{x^2-16 x+63}$, \quad $y'=\dfrac{8 x^2-97 x+260}{\sqrt{x^2-16 x+63}}$. \hfill Answer. $x=4.$ \item $y = (4 x+2)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{8 x^2+50 x+68}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-2.$ \item $y = (4 x+2)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{8 x^2-34 x+26}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=1.$ \item $y = (4 x+3)\cdot \sqrt{x^2-10 x+16}$, \quad $y'=\dfrac{8 x^2-57 x+49}{\sqrt{x^2-10 x+16}}$. \hfill Answer. $x=1.$ \item $y = (4 x+3)\cdot \sqrt{x^2-14 x+48}$, \quad $y'=\dfrac{8 x^2-81 x+171}{\sqrt{x^2-14 x+48}}$. \hfill Answer. $x=3.$ \item $y = (4 x+4)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{4 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (4 x+4)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{2 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (4 x+6)\cdot \sqrt{x^2-4 x+3}$, \quad $y'=\dfrac{2 x (4 x-9)}{\sqrt{x^2-4 x+3}}$. \hfill Answer. $x=0.$ \item $y = (4 x+7)\cdot \sqrt{x^2-8 x+7}$, \quad $y'=\dfrac{x (8 x-41)}{\sqrt{x^2-8 x+7}}$. \hfill Answer. $x=0.$ \item $y = (4 x+7)\cdot \sqrt{x^2-12 x+35}$, \quad $y'=\dfrac{8 x^2-65 x+98}{\sqrt{x^2-12 x+35}}$. \hfill Answer. $x=2.$ \item $y = (4 x+8)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{8 x^2-52 x+44}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=1.$ \item $y = (4 x+8)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{2 \left(4 x^2-35 x+54\right)}{\sqrt{x^2-13 x+40}}$. \hfill Answer. $x=2.$ \item $y = (5 x-5)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{5 \left(2 x^2-25 x+68\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=4.$ \item $y = (5 x-3)\cdot \sqrt{x^2+7 x+10}$, \quad $y'=\dfrac{20 x^2+99 x+79}{2 \sqrt{x^2+7 x+10}}$. \hfill Answer. $x=-1.$ \item $y = (5 x-3)\cdot \sqrt{x^2-11 x+30}$, \quad $y'=\dfrac{20 x^2-171 x+333}{2 \sqrt{x^2-11 x+30}}$. \hfill Answer. $x=3.$ \item $y = (5 x-2)\cdot \sqrt{x^2+9 x+20}$, \quad $y'=\dfrac{20 x^2+131 x+182}{2 \sqrt{x^2+9 x+20}}$. \hfill Answer. $x=-2.$ \item $y = (5 x-2)\cdot \sqrt{x^2-9 x+18}$, \quad $y'=\dfrac{20 x^2-139 x+198}{2 \sqrt{x^2-9 x+18}}$. \hfill Answer. $x=2.$ \item $y = (5 x+2)\cdot \sqrt{x^2-9 x+20}$, \quad $y'=\dfrac{20 x^2-131 x+182}{2 \sqrt{x^2-9 x+20}}$. \hfill Answer. $x=2.$ \item $y = (5 x+3)\cdot \sqrt{x^2-7 x+10}$, \quad $y'=\dfrac{20 x^2-99 x+79}{2 \sqrt{x^2-7 x+10}}$. \hfill Answer. $x=1.$ \item $y = (5 x+4)\cdot \sqrt{x^2-12 x+20}$, \quad $y'=\dfrac{2 \left(5 x^2-43 x+38\right)}{\sqrt{x^2-12 x+20}}$. \hfill Answer. $x=1.$ \item $y = (5 x+4)\cdot \sqrt{x^2-18 x+80}$, \quad $y'=\dfrac{10 x^2-131 x+364}{\sqrt{x^2-18 x+80}}$. \hfill Answer. $x=4.$ \item $y = (5 x+5)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{5 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (5 x+5)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{2 \sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (5 x+6)\cdot \sqrt{x^2-14 x+40}$, \quad $y'=\dfrac{10 x^2-99 x+158}{\sqrt{x^2-14 x+40}}$. \hfill Answer. $x=2.$ \item $y = (5 x+6)\cdot \sqrt{x^2-16 x+60}$, \quad $y'=\dfrac{2 \left(5 x^2-57 x+126\right)}{\sqrt{x^2-16 x+60}}$. \hfill Answer. $x=3.$ \item $y = (5 x+7)\cdot \sqrt{x^2-7 x+12}$, \quad $y'=\dfrac{20 x^2-91 x+71}{2 \sqrt{x^2-7 x+12}}$. \hfill Answer. $x=1.$ \item $y = (5 x+8)\cdot \sqrt{x^2-5 x+4}$, \quad $y'=\dfrac{x (20 x-59)}{2 \sqrt{x^2-5 x+4}}$. \hfill Answer. $x=0.$ \item $y = (5 x+9)\cdot \sqrt{x^2-10 x+9}$, \quad $y'=\dfrac{2 x (5 x-33)}{\sqrt{x^2-10 x+9}}$. \hfill Answer. $x=0.$ \item $y = (5 x+9)\cdot \sqrt{x^2-16 x+63}$, \quad $y'=\dfrac{10 x^2-111 x+243}{\sqrt{x^2-16 x+63}}$. \hfill Answer. $x=3.$ \item $y = (5 x+10)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{5 \left(2 x^2-13 x+11\right)}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=1.$ \item $y = (5 x+10)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{5 \left(4 x^2-35 x+54\right)}{2 \sqrt{x^2-13 x+40}}$. \hfill Answer. $x=2.$ \item $y = (6 x-4)\cdot \sqrt{x^2-7 x+12}$, \quad $y'=\dfrac{12 x^2-67 x+86}{\sqrt{x^2-7 x+12}}$. \hfill Answer. $x=2.$ \item $y = (6 x-3)\cdot \sqrt{x^2+6 x+8}$, \quad $y'=\dfrac{3 \left(4 x^2+17 x+13\right)}{\sqrt{x^2+6 x+8}}$. \hfill Answer. $x=-1.$ \item $y = (6 x-3)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{3 \left(4 x^2-25 x+34\right)}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=2.$ \item $y = (6 x-2)\cdot \sqrt{x^2+5 x+6}$, \quad $y'=\dfrac{12 x^2+43 x+31}{\sqrt{x^2+5 x+6}}$. \hfill Answer. $x=-1.$ \item $y = (6 x-2)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{4 \left(3 x^2-23 x+34\right)}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=2.$ \item $y = (6 x-2)\cdot \sqrt{x^2-12 x+35}$, \quad $y'=\dfrac{2 \left(6 x^2-55 x+111\right)}{\sqrt{x^2-12 x+35}}$. \hfill Answer. $x=3.$ \item $y = (6 x+2)\cdot \sqrt{x^2-5 x+6}$, \quad $y'=\dfrac{12 x^2-43 x+31}{\sqrt{x^2-5 x+6}}$. \hfill Answer. $x=1.$ \item $y = (6 x+3)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{3 \left(4 x^2+25 x+34\right)}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-2.$ \item $y = (6 x+3)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{3 \left(4 x^2-17 x+13\right)}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=1.$ \item $y = (6 x+4)\cdot \sqrt{x^2+7 x+12}$, \quad $y'=\dfrac{12 x^2+67 x+86}{\sqrt{x^2+7 x+12}}$. \hfill Answer. $x=-2.$ \item $y = (6 x+4)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{4 \left(3 x^2-17 x+14\right)}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=1.$ \item $y = (6 x+4)\cdot \sqrt{x^2-10 x+24}$, \quad $y'=\dfrac{2 \left(6 x^2-43 x+62\right)}{\sqrt{x^2-10 x+24}}$. \hfill Answer. $x=2.$ \item $y = (6 x+6)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{6 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (6 x+6)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{3 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (6 x+8)\cdot \sqrt{x^2-3 x+2}$, \quad $y'=\dfrac{x (12 x-19)}{\sqrt{x^2-3 x+2}}$. \hfill Answer. $x=0.$ \item $y = (6 x+9)\cdot \sqrt{x^2-4 x+3}$, \quad $y'=\dfrac{3 x (4 x-9)}{\sqrt{x^2-4 x+3}}$. \hfill Answer. $x=0.$ \item $y = (6 x+10)\cdot \sqrt{x^2+9 x+20}$, \quad $y'=\dfrac{12 x^2+91 x+165}{\sqrt{x^2+9 x+20}}$. \hfill Answer. $x=-3.$ \item $y = (6 x+10)\cdot \sqrt{x^2-6 x+5}$, \quad $y'=\dfrac{4 x (3 x-11)}{\sqrt{x^2-6 x+5}}$. \hfill Answer. $x=0.$ \item $y = (6 x+10)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{2 \left(6 x^2-31 x+25\right)}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=1.$ \item $y = (7 x-4)\cdot \sqrt{x^2-15 x+56}$, \quad $y'=\dfrac{28 x^2-323 x+844}{2 \sqrt{x^2-15 x+56}}$. \hfill Answer. $x=4.$ \item $y = (7 x-2)\cdot \sqrt{x^2-11 x+24}$, \quad $y'=\dfrac{28 x^2-235 x+358}{2 \sqrt{x^2-11 x+24}}$. \hfill Answer. $x=2.$ \item $y = (7 x-1)\cdot \sqrt{x^2-13 x+40}$, \quad $y'=\dfrac{28 x^2-275 x+573}{2 \sqrt{x^2-13 x+40}}$. \hfill Answer. $x=3.$ \item $y = (7 x+3)\cdot \sqrt{x^2-13 x+42}$, \quad $y'=\dfrac{28 x^2-267 x+549}{2 \sqrt{x^2-13 x+42}}$. \hfill Answer. $x=3.$ \item $y = (7 x+5)\cdot \sqrt{x^2-9 x+14}$, \quad $y'=\dfrac{28 x^2-179 x+151}{2 \sqrt{x^2-9 x+14}}$. \hfill Answer. $x=1.$ \item $y = (7 x+6)\cdot \sqrt{x^2-11 x+28}$, \quad $y'=\dfrac{28 x^2-219 x+326}{2 \sqrt{x^2-11 x+28}}$. \hfill Answer. $x=2.$ \item $y = (7 x+7)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{7 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (7 x+7)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{7 \left(4 x^2-43 x+93\right)}{2 \sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (7 x+10)\cdot \sqrt{x^2-11 x+30}$, \quad $y'=\dfrac{28 x^2-211 x+310}{2 \sqrt{x^2-11 x+30}}$. \hfill Answer. $x=2.$ \item $y = (8 x-4)\cdot \sqrt{x^2+6 x+8}$, \quad $y'=\dfrac{4 \left(4 x^2+17 x+13\right)}{\sqrt{x^2+6 x+8}}$. \hfill Answer. $x=-1.$ \item $y = (8 x-4)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{4 \left(4 x^2-25 x+34\right)}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=2.$ \item $y = (8 x-2)\cdot \sqrt{x^2-12 x+27}$, \quad $y'=\dfrac{2 \left(8 x^2-73 x+114\right)}{\sqrt{x^2-12 x+27}}$. \hfill Answer. $x=2.$ \item $y = (8 x-2)\cdot \sqrt{x^2-16 x+63}$, \quad $y'=\dfrac{2 \left(8 x^2-97 x+260\right)}{\sqrt{x^2-16 x+63}}$. \hfill Answer. $x=4.$ \item $y = (8 x+4)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{4 \left(4 x^2+25 x+34\right)}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-2.$ \item $y = (8 x+4)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{4 \left(4 x^2-17 x+13\right)}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=1.$ \item $y = (8 x+6)\cdot \sqrt{x^2-10 x+16}$, \quad $y'=\dfrac{2 \left(8 x^2-57 x+49\right)}{\sqrt{x^2-10 x+16}}$. \hfill Answer. $x=1.$ \item $y = (8 x+6)\cdot \sqrt{x^2-14 x+48}$, \quad $y'=\dfrac{2 \left(8 x^2-81 x+171\right)}{\sqrt{x^2-14 x+48}}$. \hfill Answer. $x=3.$ \item $y = (8 x+8)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{8 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (8 x+8)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{4 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (9 x-5)\cdot \sqrt{x^2-19 x+90}$, \quad $y'=\dfrac{36 x^2-523 x+1715}{2 \sqrt{x^2-19 x+90}}$. \hfill Answer. $x=5.$ \item $y = (9 x-3)\cdot \sqrt{x^2+5 x+6}$, \quad $y'=\dfrac{3 \left(12 x^2+43 x+31\right)}{2 \sqrt{x^2+5 x+6}}$. \hfill Answer. $x=-1.$ \item $y = (9 x-3)\cdot \sqrt{x^2-10 x+21}$, \quad $y'=\dfrac{6 \left(3 x^2-23 x+34\right)}{\sqrt{x^2-10 x+21}}$. \hfill Answer. $x=2.$ \item $y = (9 x-3)\cdot \sqrt{x^2-12 x+35}$, \quad $y'=\dfrac{3 \left(6 x^2-55 x+111\right)}{\sqrt{x^2-12 x+35}}$. \hfill Answer. $x=3.$ \item $y = (9 x-2)\cdot \sqrt{x^2-13 x+30}$, \quad $y'=\dfrac{36 x^2-355 x+566}{2 \sqrt{x^2-13 x+30}}$. \hfill Answer. $x=2.$ \item $y = (9 x+1)\cdot \sqrt{x^2-15 x+50}$, \quad $y'=\dfrac{36 x^2-403 x+885}{2 \sqrt{x^2-15 x+50}}$. \hfill Answer. $x=3.$ \item $y = (9 x+3)\cdot \sqrt{x^2-5 x+6}$, \quad $y'=\dfrac{3 \left(12 x^2-43 x+31\right)}{2 \sqrt{x^2-5 x+6}}$. \hfill Answer. $x=1.$ \item $y = (9 x+4)\cdot \sqrt{x^2-17 x+72}$, \quad $y'=\dfrac{36 x^2-451 x+1228}{2 \sqrt{x^2-17 x+72}}$. \hfill Answer. $x=4.$ \item $y = (9 x+6)\cdot \sqrt{x^2+7 x+12}$, \quad $y'=\dfrac{3 \left(12 x^2+67 x+86\right)}{2 \sqrt{x^2+7 x+12}}$. \hfill Answer. $x=-2.$ \item $y = (9 x+6)\cdot \sqrt{x^2-8 x+12}$, \quad $y'=\dfrac{6 \left(3 x^2-17 x+14\right)}{\sqrt{x^2-8 x+12}}$. \hfill Answer. $x=1.$ \item $y = (9 x+6)\cdot \sqrt{x^2-10 x+24}$, \quad $y'=\dfrac{3 \left(6 x^2-43 x+62\right)}{\sqrt{x^2-10 x+24}}$. \hfill Answer. $x=2.$ \item $y = (9 x+7)\cdot \sqrt{x^2-11 x+18}$, \quad $y'=\dfrac{36 x^2-283 x+247}{2 \sqrt{x^2-11 x+18}}$. \hfill Answer. $x=1.$ \item $y = (9 x+9)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{9 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (9 x+9)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{9 \left(4 x^2-43 x+93\right)}{2 \sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$ \item $y = (9 x+10)\cdot \sqrt{x^2-13 x+36}$, \quad $y'=\dfrac{36 x^2-331 x+518}{2 \sqrt{x^2-13 x+36}}$. \hfill Answer. $x=2.$ \item $y = (10 x-5)\cdot \sqrt{x^2+6 x+8}$, \quad $y'=\dfrac{5 \left(4 x^2+17 x+13\right)}{\sqrt{x^2+6 x+8}}$. \hfill Answer. $x=-1.$ \item $y = (10 x-5)\cdot \sqrt{x^2-8 x+15}$, \quad $y'=\dfrac{5 \left(4 x^2-25 x+34\right)}{\sqrt{x^2-8 x+15}}$. \hfill Answer. $x=2.$ \item $y = (10 x-4)\cdot \sqrt{x^2+9 x+20}$, \quad $y'=\dfrac{20 x^2+131 x+182}{\sqrt{x^2+9 x+20}}$. \hfill Answer. $x=-2.$ \item $y = (10 x-4)\cdot \sqrt{x^2-9 x+18}$, \quad $y'=\dfrac{20 x^2-139 x+198}{\sqrt{x^2-9 x+18}}$. \hfill Answer. $x=2.$ \item $y = (10 x+4)\cdot \sqrt{x^2-9 x+20}$, \quad $y'=\dfrac{20 x^2-131 x+182}{\sqrt{x^2-9 x+20}}$. \hfill Answer. $x=2.$ \item $y = (10 x+5)\cdot \sqrt{x^2+8 x+15}$, \quad $y'=\dfrac{5 \left(4 x^2+25 x+34\right)}{\sqrt{x^2+8 x+15}}$. \hfill Answer. $x=-2.$ \item $y = (10 x+5)\cdot \sqrt{x^2-6 x+8}$, \quad $y'=\dfrac{5 \left(4 x^2-17 x+13\right)}{\sqrt{x^2-6 x+8}}$. \hfill Answer. $x=1.$ \item $y = (10 x+6)\cdot \sqrt{x^2-7 x+10}$, \quad $y'=\dfrac{20 x^2-99 x+79}{\sqrt{x^2-7 x+10}}$. \hfill Answer. $x=1.$ \item $y = (10 x+8)\cdot \sqrt{x^2-12 x+20}$, \quad $y'=\dfrac{4 \left(5 x^2-43 x+38\right)}{\sqrt{x^2-12 x+20}}$. \hfill Answer. $x=1.$ \item $y = (10 x+8)\cdot \sqrt{x^2-18 x+80}$, \quad $y'=\dfrac{20 x^2-262 x+728}{\sqrt{x^2-18 x+80}}$. \hfill Answer. $x=4.$ \item $y = (10 x+10)\cdot \sqrt{x^2-12 x+32}$, \quad $y'=\dfrac{10 \left(2 x^2-17 x+26\right)}{\sqrt{x^2-12 x+32}}$. \hfill Answer. $x=2.$ \item $y = (10 x+10)\cdot \sqrt{x^2-15 x+54}$, \quad $y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. \hfill Answer. $x=3.$
\end{enumerate}
\end{document} 

Now I want to align derivative. I tried

\documentclass{article}
\usepackage{amsmath}
\usepackage{longtable}
\usepackage{booktabs}
\begin{document}
\begin{longtable}{p{0.5cm}p{5cm}p{5cm}p{3cm}}
\toprule
Oder& The function    & Derivative of the function    & Solution of Derivative \\
\midrule
1&$y = (10 x+10)\cdot \sqrt{x^2-15 x+54}$ & $y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. & $x=3.$ \\
2&$y = (10 x+10)\cdot \sqrt{x^2-15 x+54}$ & $y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. & $x=3.$ \\
3& $y = (10 x+10)\cdot \sqrt{x^2-15 x+54}$ & $y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}}$. & $x=3.$ \\
4& $y = (10 x+8)\cdot \sqrt{x^2-18 x+80}$. & $y'=\dfrac{20 x^2-262 x+728}{\sqrt{x^2-18 x+80}}$& $x=4.$\\
\bottomrule

\end{longtable}
\end{document}

How can I align this enumerate?

  • what is the question exactly? {p{0.5cm}p{5cm}p{5cm}p{3cm}} is wider than the page so you need narrower columns. (it's easier to specify the width in pt rather than cm as then when tex reports how wide the table is you can easily adjust. You have to make the table 87pt (2cm or so) less wide as TeX warns:Overfull \hbox (87.11218pt too wide) in alignment at lines 6--16 – David Carlisle Sep 20 '16 at 8:58
7

You need to make the table fit inside the textblock. Some suggestions/observations:

  • There seems to be no need for fixed-width columns. Use c instead.

  • Move repeated pieces of information -- y=, y'=, and x= -- out of the body of the text and into the header.

  • Omit all punctuation marks and \cdot directives. Doing so will help declutter the appearance of the table.

  • Insert a bit more space between the rows, say, via \addlinespace instructions.


\documentclass{article}
\usepackage{amsmath,longtable,booktabs,array}
\newcolumntype{C}{>{$}c<{$}} % automatic-mathmode version of "c"
\begin{document}
\begin{longtable}{@{}lCCC@{}}
\toprule
Order& \text{Function $y$} & \text{Derivative $y'$} & \text{Solution $x$} \\
\midrule
1 & (10 x+10) \sqrt{x^2-15 x+54} & \dfrac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
2 & (10 x+10) \sqrt{x^2-15 x+54} & \dfrac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
3 & (10 x+10) \sqrt{x^2-15 x+54} & \dfrac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
4 & (10 x+8) \sqrt{x^2-18 x+80}  & \dfrac{20 x^2-262 x+728}{\sqrt{x^2-18 x+80}}  & 4 \\
\bottomrule

\end{longtable}
\end{document} 

Addendum: Here's a version of the longtable which (a) automatically inserts the row number in the first column and (b) provides more structure via \endfirsthead, \endhead, \endfoot, and \endlastfoot instructions. (Of course, the \endfoot and \endhead instructions don't come into play in the example code shown below, as the entire table fits on a single page.)

enter image description here

\documentclass{article}
\usepackage{amsmath,longtable,booktabs,array,etoolbox}
\newcolumntype{C}{>{$\displaystyle}c<{$}} % automatic math mode version of "c"
\newcounter{rownum}
\newcolumntype{N}{>{\stepcounter{rownum}\therownum}l}
\AtBeginEnvironment{longtable}{\setcounter{rownum}{0}}
\begin{document}

\begin{longtable}{@{} N CCC @{}}
%% Header information, first page
\toprule
\multicolumn{1}{@{}l}{Order}& \text{Function $y(x)$} & \text{Derivative $y'(x)$} & \text{Value of $x$ for} \\
\multicolumn{1}{@{}l}{} & & & \text{which $y'=0$} \\
\midrule
\endfirsthead

%% Header information, all pages but first
\multicolumn{4}{@{}l}{\footnotesize\em(continued from previous page)}\\
\midrule[\heavyrulewidth]
\multicolumn{1}{@{}l}{Order}& \text{Function $y(x)$} & \text{Derivative $y'(x)$} & \text{Value of $x$ for} \\
\multicolumn{1}{@{}l}{} & & & \text{which $y'=0$}\\
\midrule
\endhead

%% Footer information, all pages but final page
\midrule[\heavyrulewidth]
\multicolumn{4}{r@{}}{\footnotesize\em(continued on following page)}\\
\endfoot

%% Footer information, final page
\bottomrule
\endlastfoot

%% Body of longtable
& (10 x+10) \sqrt{x^2-15 x+54} & \frac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
& (10 x+10) \sqrt{x^2-15 x+54} & \frac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
& (10 x+10) \sqrt{x^2-15 x+54} & \frac{5 (4 x^2-43 x+93)}{\sqrt{x^2-15 x+54}} & 3 \\ 
\addlinespace
& (10 x+8) \sqrt{x^2-18 x+80}  & \frac{20 x^2-262 x+728}{\sqrt{x^2-18 x+80}}  & 4\\
\end{longtable}

\end{document} 
  • With this way, how can I number each row automatically? Because I have 174 rows. – minhthien_2016 Sep 20 '16 at 9:35
  • @toandhsp - I've provided an addendum with a longtable that automatically inserts a row number. – Mico Sep 20 '16 at 10:25
  • If in my document have many longtable and number of columns of each longtable are difference. Can you write a general code for every cases? – minhthien_2016 Sep 22 '16 at 1:15
  • @toandhsp - I'm afraid I'm not sure what your new objective is. Please consider posting a new query, in which you state what it is you're trying to achieve. By posting a new query, it will be seen by many more people, raising the odds that somebody may be able to furnish a helpful answer. – Mico Sep 22 '16 at 4:52
5

An variation of Mico answer:

\documentclass{article}
\usepackage{amsmath}
\usepackage{array,booktabs,makecell,longtable}

\newcommand\mc[1]{\multicolumn{1}{c}{\text{#1}}}
\newcounter{order}
\newcommand{\order}{\stepcounter{order}\theorder}

\usepackage{showframe}
\renewcommand*\ShowFrameColor{\color{red}}

\begin{document}
{% <-- for limiting \setcellgapes{3pt}\makegapedcells to this table only   
    \setcellgapes{3pt}
    \makegapedcells
\begin{longtable}{>{\order}c
                *{3}{>{$}l<{$}}
                  }
    \toprule
\mc{Oder}
    &    \mc{Function}    
            &   \mc{Derivative}    
                &   \mc{Solution}  \\

\midrule
   &   y = (10 x+10) \sqrt{x^2-15 x+54}
        &   y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}} 
            &   x=3                             \\
   &   y = (10 x+10) \sqrt{x^2-15 x+54}
        &   y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}} 
            &   x=3                             \\
   &   y = (10 x+10) \sqrt{x^2-15 x+54}
        &   y'=\dfrac{5 \left(4 x^2-43 x+93\right)}{\sqrt{x^2-15 x+54}} 
            &   x=3                             \\
   &   y = (10 x+8) \sqrt{x^2-18 x+80} 
        &   y'=\dfrac{20 x^2-262 x+728}{\sqrt{x^2-18 x+80}}
            &   x=4                             \\
    \bottomrule
\end{longtable}
}
\end{document}

For more space I used macros \setcellgapes{3pt} \makegapedcells from \makecells package, for numbering of equation serve macro order. Others is equal as at Mivo answer.

enter image description here

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