当x取什么值时,一元二次多项式2x²-3(x-2)²的值等于6

题目

当x取什么值时,一元二次多项式2x²-3(x-2)²的值等于6

答案

2x² - 3(x-2)² = 6
2x² - 3(x² - 4x+4) - 6 = 0
2x² - 3x² + 12x - 12 - 6 = 0
- x² + 12x - 18 = 0
x² - 12x + 18 = 0
x² - 12x + 36 = 18
(x - 6)² = 18
x - 6 = ±3√2
x = 6±3√2