Question

已知a-1/a=2,求a^2+1/a^2及a^4+1/a^4的值

Answer 1

（a-1/a）²=2²,
a²-2+1/a²=4
a²+1/a²=6
（a²+1/a²）²=6²
a^4+2+1/a^4=36
a^4+1/a^4=34

Answer 2

a^2+1/a^2=a^2-2+1/a^2+2=(a-1/a)^2+2=2^2+2=6
a^4+1/a^4=a^4+2+1/a^4-2=(a^2+1/a^2)^2-2=6^2-2=34