高手快快來~幫解數學題目

x² - 5x + 2√(x² - 5x + 3) = 12
(x² - 5x + 3) + 2√(x² - 5x + 3) - 15 = 0
[√(x² - 5x + 3)]² + 2√(x² - 5x + 3) - 15 = 0


設 u = √(x² - 5x + 3)，以上方程改式寫為：
u² + 2u - 15 = 0
(u + 5)(u - 3) = 0
u = -5 或 u = 3
√(x² - 5x + 3) = -5(捨棄) 或√(x² - 5x + 3) = 3

√(x² - 5x + 3) = 3
x² - 5x + 3 = 9
x² - 5x - 6 = 0

方程 ax² + bx + c = 0 的兩根之和為 -b/a。

故此，兩根之和
= -(-5)/1
= 5

或：
x² - 5x - 6 = 0
(x - 2)(x - 3) = 0
x = 2 或 x = 3

兩根之和
= 2 + 3
= 5

TO:賣女孩的火柴
應是筆誤
該改為以下做法

x² - 5x - 6 = 0
(x - 6)(x+1) = 0
x = 6 或 x =-1

兩根之和
= 6+(-1)= 5