Résolution d'équations

Produit, quotient, carré …


Résoudre les équations:

  1. $ (E_1):\ (2x-3)(-x+2)=0$
  2. $ (E_2):\ (x^2-5)(3x+7)=0$
  3. $ (E_3):\ (2x-3)(x+6)-(x+6)=0$
  4. $ (E_4):\ \dfrac{x^2-25}{2x-10}=0$
  5. $ (E_5):\ \dfrac{2}{2x+5}-\dfrac{1}{4x-3}=0$
  6. $ (E_6):\ (2x+3)^2=49$

Solution:


  1. $ (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\}}
$


  2. $ (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\}}$


  3. $ (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\}}$


  4. $ (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\}}$


  5. $ (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\}}$

  6. $ (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\}}$


Autres ressources