Resoudre les equations suivante 1.(-7x +2)(4x -7)=0 2.(-x +2)(2x -1)-(2x -1)=0 3.(2x +1)²-(x +3)²=0 4. 6x² -1=0

(-7x +2)(4x -7)=0.
-7x +2 = 0                        4x-7 =0
-7x = -2                            4x = 7
x = -2/-7                              x = 7/4
x = 2/7

(-x +2)(2x -1)-(2x -1)=0
(2x-1)(-x+2-1) = 0
(2x-1)(-x+1) =0

2x-1 = 0                            -x +1 =0
2x =1                                    -x = -1
x = 1/2                                   x = 1

(2x +1)²-(x +3)²=0
(2x+1-x-3)(2x+1+x+3) = 0
(x -2)(3x+4) =0

x-2 = 0                                3x+4 =0
x = 2                                    3x = -4
                                                x = -4/3

6x² -1=0
6(x-1/6)(x+1/6) = 0

x -1/6 =0                          x +1/6 = 0
x = 1/6                              x = -1/6

1) [tex](-7x+2)(4x-7)=0[/tex]
ssi [tex]-7x+2=0[/tex] ou [tex]4x-7=0[/tex]
ssi [tex]x= \frac{2}{7} [/tex] ou [tex]x= \frac{7}{4} [/tex]
donc l'equation a 2 solutions: [tex] \frac{2}{7} [/tex] et [tex] \frac{7}{4} [/tex]

2) [tex](-x+2)(2x-1)-(2x-1)=0[/tex]
ssi [tex](2x-1)[(-x+2)-1]= 0[/tex]
ssi [tex](2x-1)(-x+1)=0[/tex]
ssi [tex]2x-1=0[/tex] ou [tex]-x+1=0[/tex]
ssi [tex]x= \frac{1}{2} [/tex] ou [tex]x=1[/tex]
donc l'equation a 2 solutions: [tex] \frac{1}{2} [/tex] et [tex]x=1[/tex]

3) [tex] (2x+1)^{2}- (x+3)^{2} =0[/tex]
ssi [tex][(2x+1)-(x+3)]*[(2x+1)+(x+3)]=0[/tex]
ssi [tex](x-2)*(3x+4)=0[/tex]
ssi [tex]x-2=0[/tex] ou [tex]3x+4=0[/tex]
ssi [tex]x=2[/tex] ou [tex]x= \frac{-4}{3} [/tex]
donc l'equation a 2 solutions: [tex]2[/tex] et [tex] \frac{-4}{3} [/tex]

4) [tex]6 x^{2} -1=0[/tex]
ssi [tex] 6x^{2} - 1^{2} =0[/tex]
ssi [tex]( \sqrt{6} x-1)*( \sqrt{6} x+1)=0[/tex]
ssi [tex] \sqrt{6} x-1=0[/tex] ou [tex] \sqrt{6} x+1=0[/tex]
ssi [tex]x= \frac{1}{ \sqrt{6}} [/tex] ou [tex]x= \frac{-1}{ \sqrt{6} } [/tex]
donc l'equation a 2 solutions: [tex]\frac{1}{ \sqrt{6}} [/tex] et  [tex]\frac{-1}{ \sqrt{6} } [/tex]