1) (2x - 3)² - (x - 1)² = 0
(2x - 3 - x + 1)(2x - 3 + x - 1) = 0
(x - 2)(3x - 4) = 0
x - 2 = 0 hoặc 3x - 4 = 0
*) x - 2 = 0
x = 2
*) 3x - 4 = 0
3x = 4
Vậy:
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2) (2x + 1)² - (x - 1)² = 0
(2x + 1 - x + 1)(2x + 1 + x - 1) = 0
(x + 2).3x = 0
3x = 0 hoặc x + 2 = 0
*) 3x = 0
x = 0
*) x + 2 = 0
x = -2
Vậy x = -2; x = 0
3) (3x - 5)² - (x + 1)² = 0
(3x - 5 - x - 1)(3x - 5 + x + 1) = 0
(2x - 6)(4x - 4) = 0
2x - 6 = 0 hoặc 4x - 4 = 0
*) 2x - 6 = 0
2x = 6
x = 6 : 2
x = 3
*) 4x - 4 = 0
4x = 4
x = 4 : 4
x = 1
Vậy x = 1; x = 3
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4) (x + 2)² - (2x - 5)² = 0
(x + 2 - 2x + 5)(x + 2 + 2x - 5) = 0
(-x + 7)(3x - 3) = 0
-x + 7 = 0 hoặc 3x - 3 = 0
*) -x + 7 = 0
-x = -7
x = 7
*) 3x - 3 = 0
3x = 3
x = 3 : 3
x = 1
Vậy x =1; x = 7
5) (3x - 5)² - (x + 5)² = 0
(3x - 5 - x - 5)(3x - 5 + x + 5) = 0
(2x - 10).4x = 0
4x = 0 hoặc 2x - 10 = 0
*) 4x = 0
x = 0
*) 2x - 10 = 0
2x = 10
x = 10 : 2
x = 5
Vậy x = 0; x = 5
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6) (2x - 3)² = (x + 5)²
(2x - 3)² - (x + 5)² = 0
(2x - 3 - x - 5)(2x - 3 + x + 5) = 0
(x - 8)(3x + 2) = 0
x - 8 = 0 hoặc 3x + 2 = 0
*) x - 8 = 0
x = 8
3x + 2 = 0
3x = -2
Vậy:
7) (3x - 4)² = (x + 2)²
(3x - 4)² - (x + 2)² = 0
(3x - 4 - x - 2)(3x - 4 + x + 2) = 0
(2x - 6)(4x - 2) = 0
2x - 6 = 0 hoặc 4x - 2 = 0
*) 2x - 6 = 0
2x = 6
x = 6 : 2
x = 3
*) 4x - 2 = 0
4x = 2
Vậy 
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8) x² - 8x + 16 = 5(4 - x)³
(x - 4)² = 5(4 - x)³
(x - 4)² - 5(4 - x)³ = 0
(4 - x)² - 5(4 - x)³ = 0
(4 - x)²[1 - 5(4 - x)] = 0
(4 - x)²(1 - 20 + 5x) = 0
(4 - x)²(5x - 19) = 0
(4 - x)² = 0 hoặc 5x - 19 = 0
*) (4 - x)² = 0
4 - x = 0
x = 4
*) 5x - 19 = 0
5x = 19
Vậy:
9) (2 - x)³ = 6x(x - 2)
(2 - x)³ - 6x(x - 2) = 0
(2 - x)³ + 6x(2 - x) = 0
(2 - x)[(2 - x)² + 6x] = 0
(2 - x)(4 - 4x + x² + 6x) = 0
(2 - x)(x² + 2x + 1 + 3) = 0
(2 - x)[(x + 1)² + 3] = 0
2 - x = 0 hoặc (x + 1)² + 3 = 0
*) 2 - x = 0
x = 2
*) (x + 1)² + 3 = 0
(x + 1)² = -3 (vô lý)
Vậy x = 2
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10) x² - 3x - 10 = 0
x² + 2x - 5x - 10 = 0
(x² + 2x) - (5x + 10) = 0
x(x + 2) - 5(x + 2) = 0
(x + 2)(x - 5) = 0
x + 2 = 0 hoặc x - 5 = 0
*) x + 2 = 0
x = -2
*) x - 5 = 0
x = 5
Vậy x = -2; x = 5
11) x² - 6x + 5 = 0
x² - x - 5x + 5 = 0
(x² - x) - (5x - 5) = 0
x(x - 1) - 5(x - 1) = 0
(x - 1)(x - 5) = 0
x - 1 = 0 hoặc x - 5 = 0
*) x - 1 = 0
x = 1
*) x - 5 = 0
x = 5
Vậy x = 1; x = 5
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12) x² - 3x - 10 = 0
x² - 5x + 2x - 10 = 0
(x² - 5x) + (2x - 10) = 0
x(x - 5) + 2(x - 5) = 0
(x - 5)(x + 2) = 0
x - 5 = 0 hoặc x + 2 = 0
*) x - 5 = 0
x = 5
*) x + 2 = 0
x = -2
Vậy x = -2; x = 5
13) x² - 7x + 12 = 0
x² - 3x - 4x + 12 = 0
(x² - 3x) - (4x - 12) = 0
x(x - 3) - 4(x - 3) = 0
(x - 3)(x - 4) = 0
x - 3 = 0 hoặc x - 4 = 0
*) x - 3 = 0
x = 3
*) x - 4 = 0
x = 4
Vậy x = 3; x = 4
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14) 8x² + 30x + 7 = 0
8x² + 2x + 28x + 7 = 0
(8x² + 2x) + (28x + 7) = 0
2x(4x + 1) + 7(4x + 1) = 0
(4x + 1)(2x + 7) = 0
4x + 1 = 0 hoặc 2x + 7 = 0
*) 4x + 1 = 0
4x = -1
*) 2x + 7 = 0
2x = -7
Vậy:
15) x² - 4x + 3 = 0
x² - x - 3x + 3 = 0
(x² - x) - (3x - 3) = 0
x(x - 1) - 3(x - 1) = 0
(x - 1)(x - 3) = 0
x - 1 = 0 hoặc x - 3 = 0
*) x - 1 = 0
x = 1
*) x - 3 = 0
x = 3
Vậy x = 1; x = 3
