Question

if x+1/x=4 then find the value of x cube +1/x cube

Answer 1

Dear student
$$\begin{gathered} Givenx+\frac{1}{x}=4 \\ Now,{\left(x+\frac{1}{x}\right)}^2=x^2+\frac{1}{x^2}+2 \\ \Rightarrow 4^2=x^2+\frac{1}{x^2}+2 \\ \Rightarrow x^2+\frac{1}{x^2}=14 \\ Then{x}^3+\frac{1}{x^3} \\ =\left(x+\frac{1}{x}\right)\left(x^2+\frac{1}{x^2}-3\right)\left[\because a^3+b^3=\left(a+b\right)\left(a^2+b^2-ab\right)\right] \\ =\left(4\right)\left(14-3\right) \\ =4\times 11 \\ =44 \end{gathered}$$
Regards