Question

已知x-1÷x=1,求x的8次方+1÷x的8次方的值

Answer 1

x^8 + 1/x^8 =(x^4+1/x^4)^2-2

=[(x^2+1/x^2)^2-2]^2-2

={ [(x-1/x)^2+2]^2-2 }^2 -2

=47

主要思想就是利用x^2n+1/x^2n = (x^n + 1/x^n)^2 -2 = (x^n - 1/x^n)^2 +2