已知a>0,且满足a^2+a-1=0,求值:(1)a^2+1/a^2,(2)a^4+1/a^4,(3)a+1/a.

问题描述:

已知a>0,且满足a^2+a-1=0,求值:(1)a^2+1/a^2,(2)a^4+1/a^4,(3)a+1/a.

a²+a-1=0
a+1-1/a=0
a-1/a=-1
(1)(a-1/a)²=(-1)²
a²-2+1/a²=1
a²+1/a²=3
(2) (a²+1/a²)²=3²
a^4+2+1/a^4=9
a^4+1/a^4=7
(3)a²+1/a²=3
a²+2+1/a²=5
(a+1/a)²=5
a+1/a=±√5