Question

if x = 2 + root 3 find x+1/x
Q. If $x=2+\sqrt{3}findx+\frac{1}{x}$

Answer 1

Dear Student,

$$\begin{gathered} Given:x=2+\sqrt{3} \\ So,\frac{1}{x}=\frac{1}{2+\sqrt{3}}\times \frac{2-\sqrt{3}}{2-\sqrt{3}} \\ \frac{1}{x}=\frac{2-\sqrt{3}}{4-3}\mathbf{}\left[\mathbf{U}\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{-}{\mathbf{b}}^{\mathbf{2}}\mathbf{=}\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\right] \\ \frac{1}{x}=2-\sqrt{3} \\ Now,x+\frac{1}{x}=2+\cancel{\sqrt{3}}+2-\cancel{\sqrt{3}} \\ \boxed{\mathbf{x}\mathbf{+}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{}\mathbf{=}\mathbf{4}} \end{gathered}$$

Regards