Question

If x 2 +1/x 2 =5, find the value of x 3 +1/x ​3

Answer 1

(x^2+1)/x^2=5
i.e. x^2/x^2+1/x^2=5
i.e. 1+1/x^2=5
i.e. 1/x^2=5-1=4
i.e. x^2=1/4
i.e. x=1/2 i.e. x^3=1/8 i.e. 1/x^3=8
i.e. (x^3+1)/x^3=x^3/x^3+1/x^3=1+1/x^=1+8=9