(x-3)(x눀+2x-3)=x+3 求解方程式

2025-03-01 18:18:13
推荐回答(2个)
回答1:

移项并化简,得到:
(x-3)(x+3)(x-1) - (x+3) = 0
(x+3) * [(x-3)(x-1) - 1] = 0
(x+3) * [x²-4x+3 - 1] = 0
(x+3) * [x² -4x + 4 - 2] = 0
(x+3) * [(x-2)² - 2] = 0
(x+3) * [(x-2 + √2)(x-2 - √2)] = 0
(x+3) * [x - (2-√2)] * [x - (2+√2)] = 0
那么,这个方程的解共有 3 个:
x+3 = 0,或
x-(2-√2) = 0,或
x - (2+√2) = 0

x = -3, 或 x = 2-√2, 或 x = 2+√2

回答2:

(x-3)(x+3)(x-1) = x+3
显然x = -3是一个解。
如果 x 不等于 3, 则
(x-3)(x-1) = 1
x² - 4x + 3 = 1
(x-2)² = 2
x = 2+/-√2