Đáp án+Giải thích các bước giải:
`a) 16x² - (4x - 5)² = 15`
`⇔ (4x)² - (4x - 5)² = 15`
`⇔ (4x - 4x + 5)(4x + 4x - 5) = 15`
`⇔ 5 . (8x - 5) = 15`
`⇔ 8x - 5 = 3`
`⇔ 8x = 8`
`⇔ x = 1`
Vậy `x = 1`
`b) (2x + 3)² - 4(x - 1)(x + 1) = 49`
`⇔ (4x² + 12x + 9) - 4(x² - 1) = 49`
`⇔ 4x² + 12x + 9 - 4x² + 4 = 49`
`⇔ 12x + 13 = 49`
`⇔ 12x = 36`
`⇔ x = 3`
Vậy `x = 3`
`c) (2x + 1)(1 - 2x) + (1 - 2x)² = 18`
`⇔ (1 + 2x)(1 - 2x) + (1 - 4x + 4x²) = 18`
`⇔ 1 - 4x² + 1 - 4x + 4x² = 18`
`⇔ - 4x + 2 = 18`
`⇔ - 4x = 16`
`⇔ x = - 4`
Vậy `x = - 4`
`d) 2(x + 1)² - (x - 3)(x + 3) - (x - 4)² = 0`
`⇔ 2(x² + 2x + 1) - (x² - 9) - (x² - 8x + 16) = 0`
`⇔ 2x² + 4x + 2 - x² + 9 - x² + 8x - 16 = 0`
`⇔ 4x + 8x + 2 + 9 - 16 = 0`
`⇔ 12x - 5 = 0`
`⇔ 12x = 5`
`⇔ x = \frac{5}{12}`
Vậy `x = \frac{5}{12}`
`e) (x - 5)² - x(x - 4) = 9`
`⇔ (x² - 10x + 25) - (x² - 4x) = 9`
`⇔ x² - 10x + 25 - x² + 4x = 9`
`⇔ - 6x + 25 = 9`
`⇔ - 6x = - 16`
`⇔ x = \frac{8}{3}`
Vậy `x = \frac{8}{3}`
`f) (x - 5)² + (x - 4)(1 - x) = 0`
`⇔ (x² - 10x + 25) + (x - x² - 4 + 4x) = 0`
`⇔ x² - 10x + 25 + x - x² - 4 + 4x = 0`
`⇔ - 5x + 21 = 0`
`⇔ - 5x = - 21`
`⇔ x = \frac{21}{5}`
Vậy `x = \frac{21}{5}`
