已知a²-7a-1=0,求a^4+1/a^4的值.

已知a²-7a-1=0,求a^4+1/a^4的值.
已知a²-7a-1=0,求a^4+1/a^4的值.

已知a²-7a-1=0,求a^4+1/a^4的值.


a²-7a-1=0
a²-1=7a
a-1/a=7
(a-1/a)²=7²
a²-2+1/a²=49
a²+1/a²=51
(a²+1/a²)²=51²
a^4+2+1/a^4=2601
a^4+1/a^4=2599