Answered

Bonjour, j'aurais besoin d'aide merci.

Résoudre les équations suivantes en essayant d'appliquer une méthode systématique:

a) [tex]5-(x-3)=4x-(3x-8)[/tex]
b) [tex]7(x+4)-3(x+2)=x+7[/tex]
c) [tex]2(x-1)-3(x+1)=4(x-2)[/tex]
d) [tex]5(3x-1)-(1-2x)=3(5x-2)[/tex]
e) [tex](x+2)(x+1)= (x+4)(x-5)[/tex]

à l'aide d'une factorisation:

1) [tex](x+2)^{2}=(x+2)(5x-4)[/tex]
2) [tex]9x^{2}-16=0 [/tex]
3) [tex](2x+3)^{2}=36[/tex]
4) [tex]5x^{2}-7x=0 [/tex]
5) [tex]4x^{2}-9-2(2x-3)+x(2x-3)=0[/tex]

Sagot :

a)  5 - (x - 3) = 4x - (3x - 8)
      5 - x + 3 = 4x - 3x + 8
            8 - x = x + 8
           - x -x = 8 - 8
             - 2x = 0
                 x = \frac{0}{-2}
                 x = 0.


b)             7(x + 4) - 3(x + 2) = x + 7
   7 x x + 7 x 4 - 3 x x - 3 x 2 = x + 7
                    7x + 28 - 3x - 6 = x + 7
                                4x + 22 = x + 7
                                   4x - x = 7 - 22
                                        3x = - 15
                                          x = \frac{-15}{3}
                                          x = - 5.

c)                  2(x - 1) - 3(x + 1) = 4(x - 2)
   2 x x + 2 x (-1) - 3 x x - 3 x 1 = 4 x x + 4 x (-2)
                            2x - 2 - 3x -3 = 4x - 8
                                       - x - 5 = 4x - 8
                                      -x - 4x = - 8 + 5
                                          - 5x = - 3
                                              x = \frac{-3}{-5}
                                              x = \frac{3}{5}