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Sagot :
1) (5x-4)²-(3x+7)²=0
(5x-4-3x-7)(5x-4+3x+7) =0
(2x-11)(8x+3) =0
2x-11 = 0 8x+3 =0
2x =11 8x = -3
x =11/2 x = -3/8
2) (x-2)²=1/16(5-2x)²
(x-2)²-1/16(5-2x)² =0
(x-2)² -1²/4²(5-2x)² =0
(x-2-5/4+2/4x)(x-2+5/4-2/4x) =0
(x-2-5/4+1/2x)(x-2+5/4-1/2x) =0
(2/2x -8/4-5/4+1/2x)(2/2x-8/4 +5/4-1/2x) =0
(3/2x-13/4)(1/2x-3/4) =0
3/2x -13/4 =0 1/2x-3/4 =0
3/2x = 13/4 1/2x = 3/4
x = 13/4 x2/3 x = 3/4x2
x =26/12 x = 6/4
x = 13/6 x = 3/2
3) (x+1(3-2x)=4x²-9
(x+1)(3-2x) -(4x²-9) =0
(x+1)(3-2x) -(2x-3)(2x+3)= 0
(x+1)(3-2x) +(-2x+3)(-2x+3) =0
(3-2x)(x+1-2x+3) =0
(3-2x)(-x+4) =0
3-2x =0 -x+4 =0
-2x = -3 -x =-4
x = -3/-2 = 3/2 x =4
4) (x+2)²=2(x²-4)
(x+2)²-2(x²-4) =0
(x+2)²-2(x-2)(x+2) =0
(x+2)(x+2-2x+4) =0
(x+2)(-x+6) =0
x+2 =0 -x+6 =0
x = -2 -x =-6
x =6
(5x-4-3x-7)(5x-4+3x+7) =0
(2x-11)(8x+3) =0
2x-11 = 0 8x+3 =0
2x =11 8x = -3
x =11/2 x = -3/8
2) (x-2)²=1/16(5-2x)²
(x-2)²-1/16(5-2x)² =0
(x-2)² -1²/4²(5-2x)² =0
(x-2-5/4+2/4x)(x-2+5/4-2/4x) =0
(x-2-5/4+1/2x)(x-2+5/4-1/2x) =0
(2/2x -8/4-5/4+1/2x)(2/2x-8/4 +5/4-1/2x) =0
(3/2x-13/4)(1/2x-3/4) =0
3/2x -13/4 =0 1/2x-3/4 =0
3/2x = 13/4 1/2x = 3/4
x = 13/4 x2/3 x = 3/4x2
x =26/12 x = 6/4
x = 13/6 x = 3/2
3) (x+1(3-2x)=4x²-9
(x+1)(3-2x) -(4x²-9) =0
(x+1)(3-2x) -(2x-3)(2x+3)= 0
(x+1)(3-2x) +(-2x+3)(-2x+3) =0
(3-2x)(x+1-2x+3) =0
(3-2x)(-x+4) =0
3-2x =0 -x+4 =0
-2x = -3 -x =-4
x = -3/-2 = 3/2 x =4
4) (x+2)²=2(x²-4)
(x+2)²-2(x²-4) =0
(x+2)²-2(x-2)(x+2) =0
(x+2)(x+2-2x+4) =0
(x+2)(-x+6) =0
x+2 =0 -x+6 =0
x = -2 -x =-6
x =6
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