Question

若x加x的负一次方等于3，求x的三次方加x的负三次方

Answer 1

a3+b3=(a+b)(a2-ab+b2)
x+1/x=3,(x+1/x)2=x2 + 1/x2 + 2=9;x2 + 1/x2=7
x3+1/x3=(x+1/x)(x2-1+1/x2)=3*(7-1)=18

Answer 2

x^3+x^-3=(x+x^-1)(x^2-x*x^+x^-2)=3(x^2-1+x^-2)=3(x^2+2+x^-2-3)=3[(x+x^-1)^2-3]=3(3^2-3)=18