Pour le a c'est : 3x+8 = 2x-5
3x-2x=-5-8
1x= -13
x= -13
Exercice N°1 :
a. 3x + 8 = 2x - 5
3x + 8 - 8 = 2x - 5 - 8
3x = 2x - 13
3x - 2x = 2x - 13 - 2x
x = 13
b. (2x + 3) (-5x + 1) = 0
-10x² + 2x - 15x + 3 = 0
-10x² - 13x + 3 = 0
-10x² - 13x + 3 - 3 = 0 - 3
-10x² - 13x = - 3
x = 15
c. -2 (3x + 25) = x + 10
-6x - 50 = x + 10
-6x - 50 + 50 = x + 10 + 50
-6x = x + 60
-6x - x = x + 60 - x
-7x = 60
-7x /7 = 60/7
x = 60/7
d. 4 - (x - 5)² = (x + 4)² + 37
4 - (x² - 10x + 25) = (x² + 8x + 16) + 37
4 - x² + 10x - 25 = x² + 8x + 16 + 37
- x² + 10x - 21 = x² + 8x + 53
- x² + 10x - 21 + 21 = x² + 8x + 53 + 21
- x² + 10x = x² + 8x + 74
- x² + 10x - 10x = x² + 8x + 74 - 10x
- x² = x² - 2x + 74
- x² - x² = x² - 2x + 74 - x²
- 2x² = - 2x + 74
√-2x² = √- 2x + 74
x² = 37
e. (2x - 1)² - 4 = 0
4x² - 4x + 1 - 4 = 0
4x² - 4x - 3 = 0
4x² - 4x - 3 + 3 = 0 + 3
4x² - 4x = 3
x² = 3/4
f. (3x - 1)² - (x + 2)² = 0
9x² - 6x + 1 - (x² + 4x + 4) = 0
9x² - 6x + 1 - x² - 4x - 4 = 0
8x² - 10x - 3 = 0
8x² - 10x - 3 + 3 = 0 + 3
8x² - 10x = 3
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Pour le a c'est : 3x+8 = 2x-5
3x-2x=-5-8
1x= -13
x= -13
Exercice N°1 :
a. 3x + 8 = 2x - 5
3x + 8 - 8 = 2x - 5 - 8
3x = 2x - 13
3x - 2x = 2x - 13 - 2x
x = 13
b. (2x + 3) (-5x + 1) = 0
-10x² + 2x - 15x + 3 = 0
-10x² - 13x + 3 = 0
-10x² - 13x + 3 - 3 = 0 - 3
-10x² - 13x = - 3
x = 15
c. -2 (3x + 25) = x + 10
-6x - 50 = x + 10
-6x - 50 + 50 = x + 10 + 50
-6x = x + 60
-6x - x = x + 60 - x
-7x = 60
-7x /7 = 60/7
x = 60/7
d. 4 - (x - 5)² = (x + 4)² + 37
4 - (x² - 10x + 25) = (x² + 8x + 16) + 37
4 - x² + 10x - 25 = x² + 8x + 16 + 37
- x² + 10x - 21 = x² + 8x + 53
- x² + 10x - 21 + 21 = x² + 8x + 53 + 21
- x² + 10x = x² + 8x + 74
- x² + 10x - 10x = x² + 8x + 74 - 10x
- x² = x² - 2x + 74
- x² - x² = x² - 2x + 74 - x²
- 2x² = - 2x + 74
√-2x² = √- 2x + 74
x² = 37
e. (2x - 1)² - 4 = 0
4x² - 4x + 1 - 4 = 0
4x² - 4x - 3 = 0
4x² - 4x - 3 + 3 = 0 + 3
4x² - 4x = 3
x² = 3/4
f. (3x - 1)² - (x + 2)² = 0
9x² - 6x + 1 - (x² + 4x + 4) = 0
9x² - 6x + 1 - x² - 4x - 4 = 0
8x² - 10x - 3 = 0
8x² - 10x - 3 + 3 = 0 + 3
8x² - 10x = 3