a²-7a-1=0,则a²-1=7a.显然a不为0.
方程a²-1=7a两边同除以a,得:a-1/a=7.
(1)(a-1/a)²=7²,即a²+1/a²-2=49,故a²+1/a²=51;
(2)(a²+1/a²)²=51²,即a⁴+1/a⁴+2=2601,故a⁴+1/a⁴=2599.