Question

If x2+1/x2=18, find the value of x3−1/x3

Answer 1

Please find attached photograph for your answer.

Answer 2

There are 2 answers : 76 or -76

Explanation:

`x^2+(1)/(x^2) =18\\\\(x-(1)/(x) )^2=x^2+(1)/(x^2) -2=18-2=16\\\\x-(1)/(x)=4\ or\ x-(1)/(x)-4\\\\(x-(1)/(x) )^3=x^3-(1)/(x^3) -3x^2*(1)/(x)+3x*(1)/(x^2)\\\\=x^3-(1)/(x^3)-3(x-(1)/(x))\\\\x^3-(1)/(x^3)=(x-(1)/(x) )^3+3(x-(1)/(x))\\\\if\ x-(1)/(x)=4\ then \ x^3-(1)/(x^3)=4^3+3*4=64-12=76\\\\if\ x-(1)/(x)=-4\ then \ x^3-(1)/(x^3)=(-4)^3+3*(-4)=-64-12=-76\\\\`