Message d'erreur

  • Deprecated function: Optional parameter $account declared before required parameter $entity_type is implicitly treated as a required parameter in include_once() (line 1442 of /home/senemav/www/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $account declared before required parameter $entity_type is implicitly treated as a required parameter in include_once() (line 1442 of /home/senemav/www/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $account declared before required parameter $entity_type is implicitly treated as a required parameter in include_once() (line 1442 of /home/senemav/www/includes/bootstrap.inc).
  • Deprecated function: Optional parameter $input declared before required parameter $form_state is implicitly treated as a required parameter in include_once() (line 1442 of /home/senemav/www/includes/bootstrap.inc).

Correction

Corrigé Concours d'entrée lycée d'excellence de Diourbel - Épreuve de Mathématiques - 2022

 
$\begin{array}{rcl} 1/\quad x^{2}-y^{2}&=&\left(\dfrac{\sqrt{m}+\sqrt{n}}{2}\right)^{2}-\left(\dfrac{\sqrt{m}-\sqrt{n}}{2}\right)^{2}\\&=&\dfrac{\require{cancel}\cancel{m}+2\sqrt{mn}+\require{cancel}\cancel{n}-\left(\require{cancel}\cancel{m}-2\sqrt{mn}+\require{cancel}\cancel{n}\right)}{4}\\&=&\dfrac{4\sqrt{mn}}{4}\\&=&\boxed{\sqrt{mn}} \end{array}$
 
2/ La condition de colinéarité s'écrit :
 
$|x-1|-4=0$, soit $x-1=4$ ou $x-1=-4$