Question

已知：x+x^-1=2,求 x^+x^-2和x^4+x^-4的值

Answer 1

x+x^-1=2,那么 x^2+x^-2和x^4+x^-4的值都为2

x+x^-1=2,所以(x+x^-1)^2=4,即 x^2+2+x^-2=4,所以x^2+x^-2=2；将x^2+x^-2=2等式两边平方,又得x^4+2+x^-4=4,所以x^4+x^-4=2