Question

已知x≠0,且x+（1/x）=3,求（1）x^2+1/(x^2)的值,（2）x^4+1/(x^4)的值

Answer 1

x+（1/x）=3

左右平方,二项式公式

(x+(1/x))^2=x^2+2+1/(x^2)=9

x^2+1/(x^2)=7

再平方

(x^2+1/(x^2))^2=x^4+2+1/(x^4)=49

x^4+1/(x^4)=47