Question

a²-3a+1=0,试求(a²-1/a²)(a-1/a)的值

Answer 1

∵a²-3a+1=0
∴上式两边同时除以a：
a-3+1/a=0
∴a+1/a=3
∴a²+2+1/a²=9
∴a²+1/a²=7
(a²-1/a²)(a-1/a)=(a+1/a)(a-1/a)²=(a+1/a)(a²-2+1/a²)=3*(7-2)=15