Question

若x+（1/x）=3,求（x^3+x^(-3)+7）÷（x^4+x^(-4)+3）的值

Answer 1

答案是1/2.

(x+1/x)^3=x^3+(1/x)^3+3*(x+1/x)=27 x^3+x^(-3)=27-3*3=18

(x+1/x)^4=x^4+x^(-4)+4*(x+1/x)^2-2=81 x^4+x^(-4)= 47

=(18+7)/(47=3)=1/2