题目

x+x分之1=4 求x4方减x4方分之1的值

提问时间：2021-03-12

答案

x + 1/x =4
(x +1/x)² = 16
x² + 2 + 1/x² =16
x² +1/x² = 14
(x - 1/x)² = x² -2 +1/x² = 12
x- 1/x = ±2√3
x⁴ - 1/x⁴
= (x² + 1/x²)(x² - 1/x²)
= (x²+1/x²)(x+1/x)(x-1/x)
= 14×4×(±2√3)
= ± 112√3