Question

已知x+x的-1次幂=a,求x²+x的-2次幂和x的4次幂+x的-4次幂的值

Answer 1

x+x^(-1)=a

{x+x^(-1)}^2=a^2

x^2+x^(-2)+2=a^2

x^2+x^(-2)=a^2-2

(x^2+x^(-2)}^2=(a^2-2)^2

x^4+x^(-4)+2=a^4-4a^2+4

x^4+x^(-4)=a^4-4a^2+2