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

Salut,

1.(-7x +2)(4x -7)=0
-7x + 2 = 0
-7x = -2
7x = 2
x = 2/7

4x - 7 = 0
4x = 7
x = 7/4

S = {2/7; 7/4}


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

S = {1/2; 1}

3.(2x +1)²-(x +3)²=0

[(2x+1) - (x+3)][(2x+1 + x + 3] =0
(2x + 1 - x - 3)(3x + 4) = 0
(x -2)(3x+4) = 0
x - 2 = 0
x = 2
3x + 4 = 0
3x = -4
x = -4/3

S = {-4/3; 2}

4. 6x² -1=0
6x² = 1
x² = 1/6
x² - 1/6 = 0
[tex](x+ \sqrt{\frac{1}{6} } )(x-\sqrt{\frac{1}{6} }) = 0\\ (x+ \frac{1}{ \sqrt{6} } )(x-\frac{1}{ \sqrt{6} } ) = 0\\ (x+ \frac{ \sqrt{6} }{6})(x-\frac{ \sqrt{6} }{6}) = 0 [/tex]

[tex]x + \frac{ \sqrt{6} }{6}} = 0\\ x = -\frac{ \sqrt{6} }{6}}\\ [/tex]
[tex]x -\frac{ \sqrt{6} }{6}} = 0\\ x = \frac{ \sqrt{6} }{6}}\\ [/tex]


Bonne soirée !