Question

关于x的方程x²-(k-1)x+1/4k²+1=0,若方程的两个实数根为x1 x2,且满足绝对值x1＝x2，求k值

具体过程

Answer 1

x² - (k - 1)x + k²/4 + 1 = 0
|x₁| = |x₂|
方程可化为(x - a)²的完全平方形式
x² - (k - 1)x + [- (k - 1)/2]² - [- (k - 1)/2]² + k²/4 + 1 = 0
[x - (k - 1)/2]² + (k/2 + 3/4) = 0
即k/2 + 3/4 = 0
k = - 3/2