Exercice corrigé: Résolution d'équations

Produit, quotient, carré …

Seconde générale

Exercice corrigé de mathématiques: Exercice corrigé: Résolution d'équations diverses, produit nul, quotient nul, avec un carré

Résoudre les équations:

$(E_1):\ (2x-3)(-x+2)=0 \iff \left\{\begin{array}{lll} &2x-3=0 \\ \mbox{ou,... ...eft\{\begin{array}{lll} &x=\dfrac{3}{2} \\ \mbox{ou, } &x=2\end{array}\right.$ $\underline{\mathcal{S}_1=\left\{\dfrac{3}{2}\,;\,2\right\}}$
$(E_2):\ (x^2-5)(3x+7)=0 \iff \left\{\begin{array}{lll} &x^2-5=0 \\ \mbox{o... ...t{5}\ \mbox{ou, } x=\sqrt{5} \\ \mbox{ou, } x=-\dfrac{7}{3}\end{array}\right.$
$\underline{\mathcal{S}_2=\left\{-\dfrac{7}{3}\,;\,-\sqrt{5}\,;\,\sqrt{5}\right\}}$
$(E_3):\ (2x-3)(x+6)-(x+6)=0 \iff (x+6)\Big[(2x-3)-1\Big]=0 \iff (x+6)\le... ... \iff \left\{\begin{array}{lll} &x=-6 \\ \mbox{ou, } &x=2\end{array}\right.$ $\underline{\mathcal{S}_3=\left\{-6\,;\,2\right\}}$
$(E_4):\ \dfrac{x^2-25}{2x-10}=0 \iff \left\{\begin{array}{ll} &x^2-25=0 \\ ... ...gin{array}{ll} x=-5\ \mbox{ou,}\ x=5 \\ \mbox{et, } x\not=5\end{array}\right.$ $\underline{\mathcal{S}_3=\left\{-5\right\}}$
$(E_5):\ \dfrac{2}{2x+5}-\dfrac{1}{4x-3}=0 \iff \dfrac{6x-11}{(2x+5)(4x-3)}=0... ...begin{array}{ll} &6x-11=0 \\ \mbox{et, }&(2x+5)(4x-3)\not=0\end{array}\right.$
$\iff \left\{\begin{array}{ll} &x=\dfrac{11}{6} \\ \mbox{et, }&x\not=-\dfrac{5}{2}\ \mbox{et, } x\not=\dfrac{3}{4}\end{array}\right.$ $\underline{\mathcal{S}_5=\left\{\dfrac{11}{6} \right\}}$
$(E_6):\ (2x+3)^2=49 \iff \left\{\begin{array}{lll} &2x+3=-7 \\ \mbox{ou, } &... ... \iff \left\{\begin{array}{lll} &x=-5 \\ \mbox{ou, } &x=2\end{array}\right.$ $\underline{\mathcal{S}_5=\left\{-5\,;\,2 \right\}}$

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