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Exercice 2 :

1)
3x^2 + 6x + 7 = (x-5)(3x+7)
3x^2+6x+7= 3x^2+7x-15x-35
3x^2-3x^2+6x-7x+15x=-7-35
14x = -42
x = -42/14
x = -3

2)
x^2-2x+1=3(x-1)(4x+5)
x^2-2x+1=(3x-3)(4x+5)
x^2-2x+1=12x^2+15x-12x-15
12x^2-x^2+3x+2x-15-1=0
11x^2 + 5x - 16 = 0

On calcule le discriminant :
Delta^2 = (5)^2-4*11*(-16)
Delta^2 = 25 + 704
Delta^2 = 729
Delta = V729
Delta = 27 > 0 donc 2 solutions possibles

X1 = (-5-27)/(2*11)
X1 = (-32) / 22
X1 = (-16/11)

X2 = (-5+27)/(2*11)
X2 = 22/22
X2 = 1

3)
-4(3x-1)+5(6x+8)=2(x-8)(x+1)-2x^2

-12x+4+30x+40=(2x-16)(x+1)-2x^2

18x+44=2x^2+2x-16x-16-2x^2

18x + 14x = -44 - 16
32x = -60
x = (-60) / 32
x = (-15/8)

4)
(4x-3)(5x-4)=(3x-4)(x+7)+17x^2

20x^2-16x-15x+12=3x^2+21x-4x-28+17x^2

20x^2-20x^2-31x-17x=-28-12

-48x = -40
x = (-40)/(-48)
x = 5/6

5)
16x^2 - 40x = -25
16x^2 - 40x + 25 = 0

On calcule le discriminant :
Delta^2 = (-40)^2-4*16*25
Delta^2 = 1600 - 1600 = 0
Donc une seule solution possible

x = 40/(2*16)
x = 40/32
x = 5/4

6)
16x^2 = (2x+3)^2
16x^2 - (2x+3)^2 = 0
(4x-2x-3)(4x+2x+3)=0
(2x - 3)(6x + 3) = 0

2x - 3 = 0
2x = 3
x = 3/2

6x + 3 = 0
6x = -3
x = -3/6
x = -1/2

7)
(2x + 5)^2 = 49
(2x + 5)^2 - 49 = 0
(2x + 5 - 7)(2x + 5 + 7) = 0
(2x - 2)(2x + 12) = 0

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

2x + 12 = 0
2x = -12
x = -12/2
x = -6

8)
3x^2 = 15
x^2 = 15 / 3
x^2 = 5
x = V5 ou x = -V5

9)
(2x + 5)^2 + 30 = 5
(2x + 5)^2 + 30 - 5 = 0
(2x + 5)^2 + 25 = 0
4x^2 + 20x + 25 + 25 = 0
4x^2 + 20x + 50 = 0

Delta^2 = 20^2-4*4*50
Delta^2 = 400 - 800 < 0
Donc pas de solution possible

10)
(x^2-3x)(4x-3)=x(2x+7)(x-3)

4x^3-3x^2-12x^2+9x =
(2x^2+7x)(x-3)

4x^3-3x^2-12x^2+9x =
2x^3-6x^2+7x^2-21x

4x^3-2x^3-15x^2-x^2+9x+21x= 0

2x^3 - 16x^2 + 30x = 0

2x(x^2 - 8x + 15) = 0

2x = 0
x = 0

Delta^2 = (-8)^2-4*1*15
Delta^2 = 64 - 60
Delta^2 = 4
Delta= V4
Delta = 2 > 0 deux solutions possibles

x1 = (8-2)/(2*1)
x1 = 6/2
x1 = 3

x2 = (8+2)/(2*1)
x2 = 10/2
x2 = 5