Question

root x minus 1/root x=5 find xsquare plus 1/x square

Answer 1

Dear Student,

$$\begin{gathered} \sqrt{x}-\frac{1}{\sqrt{x}}=5 \\ \Rightarrow {\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)}^2=5^2=25 \\ \Rightarrow x+\frac{1}{x}-2\left(\cancel{\sqrt{x}}\right)\left(\frac{1}{\cancel{\sqrt{x}}}\right)=25 \\ \Rightarrow x+\frac{1}{x}=25+2=27 \\ \Rightarrow {\left(x+\frac{1}{x}\right)}^2={27}^2=729 \\ \Rightarrow x^2+\frac{1}{x^2}+2\left(\cancel{x}\right)\left(\frac{1}{\cancel{x}}\right)=729 \\ \Rightarrow \boxed{{\mathbf{x}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\frac{\mathbf{1}}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{729}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathbf{}\mathbf{=}\mathbf{}\mathbf{727}\mathbf{}\mathbf{}\mathbf{}\mathbf{}} \end{gathered}$$