Question

已知:x+x^-1=4,求x²+x^-2和x^4+x^-4的值

Answer 1

(x+x^-1)^2=x²+x^-2+2x*x^-1=x²+x^-2+2=4^2=16,所以x²+x^-2=14

(x²+x^-2)^2=x^4+x^-4+2=14^2=196,所以x^4+x^-4=194