Source Latex
de la correction du devoir
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pdfauthor={Yoann Morel},
pdfsubject={Correction du devoir de mathématiques de seconde},
pdftitle={Corrigé du devoir de mathématiques de 2nde},
pdfkeywords={calcul algébrique, fractions, développer, factoriser, identités remarquables}
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\lfoot{Y. Morel - \href{https://xymaths.fr/Lycee/2nde/Mathematiques-2nde.php}{xymaths - 2nde}}
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\rfoot{Correction du devoir de mathématiques - \thepage/\pageref{LastPage}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{document}
\ct{\bf\LARGE{Corrig\'e du devoir de math\'ematiques}}
\bgex
\bigskip
$A(x)=(x+3)(2x-1)-(x+3)(x+2)
=(x+3)\Bigl[(2x-1)-(x+2)\Bigr]
=(x+3)(x-3)$
\bigskip
$B(x)=(2x+1)^2-2x(2x+1)
=(2x+1)\Bigl[(2x+1)-2x\Bigr]
=(2x+1)$
\bigskip
$C(x)=(2x+1)+(x+2)(2x+1)
=(2x+1)\Bigl(1+(x+2)\Bigr]
=(2x+1)(x+3)$
\bigskip
$D(x)=(x+3)^2-4
=(x+3)^2-2^2
=(x+3-2)(x+3+2)
=(x+1)(x+5)$
\enex
\bigskip
\bgex
\bigskip
$a=\dfrac{3x+2}{2x-3}-1=\dfrac{3x+2-(2x-3)}{2x-3}
=\dfrac{x+5}{2x-3}$
\bigskip
$b=\dfrac{x+\dfrac32}{x+\dfrac12}-1
=\dfrac{\dfrac{2x+3}2}{\dfrac{2x+1}2}-1
=\dfrac{2x+3}2\tm\dfrac2{2x+1}-1
=\dfrac{2x+3}{2x+1}-\dfrac{2x+1}{2x+1}
=\dfrac2{2x+1}$
\bigskip
$c=\dfrac{15}{\sqrt{5}}=\dfrac{15\tm\sqrt{5}}{\sqrt{5}\tm\sqrt{5}}
=\dfrac{15\sqrt{5}}{5}=3\sqrt{5}$
\bigskip
$d=\lp\sqrt{12}-\sqrt{3}\rp^2
=\lp\sqrt{12}\rp^2-2\sqrt{12}\sqrt{3}+\lp\sqrt{3}\rp^2
=12-2\sqrt{36}+3=12-12+3=3$
\bigskip
$e=(3\sqrt{2})^2-(\sqrt{2}-1)^2
=3^2\sqrt{2}^2-\lp \sqrt{2}^2-2\sqrt{2}+1^2\rp
=18-\lp 2-2\sqrt{2}+1\rp
=15+2\sqrt{2}$
\bigskip
$f=\dfrac{2}{2+\sqrt{3}}
=\dfrac{2(2-\sqrt{3})}{(2+\sqrt{3})(2-\sqrt{3})}
=2(2-\sqrt{3})$
\bigskip
%$g=\dfrac{\sqrt{3}+\sqrt{12}}{\sqrt{3}-\sqrt{12}}
%=\dfrac{(\sqrt{3}+\sqrt{12})(\sqrt{3}+\sqrt{12})}
%{(\sqrt{3}-\sqrt{12})(\sqrt{3}+\sqrt{12})}
%=\dfrac{(\sqrt{3})^2+2\sqrt{3}\sqrt{12}+(\sqrt{12})^2}{3-12}
%=\dfrac{27}{-9}=-3$
\bigskip
%$h=\dfrac{x(3x)^3}{9x^2}=\dfrac{x\tm 3^3x^3}{3^2x^2}=3x^2$
$g=(4x+12)\dfrac{\dfrac{x^2-16}{x+3}}{x-4}
=(4x+12)\dfrac{x^2-16}{x+3}\tm\dfrac1{x-4}
=4(x+3)\dfrac{(x-4)(x+4)}{x+3}\tm\dfrac1{x-4}
=4(x+4)=4x+16$
\enex
\bigskip
\label{LastPage}
\end{document}
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