Question

If x +1/x
= 10/3
find the value of x³ - 1/x³
​

Answer 1

Given,

$\bold{x+\frac{1}{x}=\frac{10}{3}}$

$\implies\bold{\frac{x^2+1}{x}=\frac{10}{3}}$

Cross multiplying,

$\implies\bold{3(x^2+1)=10x}$

$\implies\bold{3x^2+3=10x}$

$\implies\bold{3x^2-10x+3=0}$

$\implies\bold{x=3}$

Substituting the value of x to  $\bold{x^3+\frac{1}{x^3}}$

$\implies\bold{3^3+\frac{1}{3^3}}$

$\implies\bold{27 +\frac{1}{27}}$

$\boxed{\bold{\therefore\:x^3+\frac{1}{x^3}=\frac{730}{27}}}$