Question

if X=2+√3 then find {X+1/X}^3​

Answer 1

$\LARGE\textbf{\underline{\underline{Given :-}}}$

• $\large\textsf{x = 2 + √3}$

$\LARGE\textbf{\underline{\underline{To find :-}}}$

• $\large\textsf{ {(\cfrac{x + 1}{x})}^{3} }$

$\LARGE\textbf{\underline{\underline{Solution :-}}}$

$\large\textsf{= {(\cfrac{2 + √3 + 1}{2 + √3}})^{3} }$

$\large\textsf{= \cfrac{{( 2 + √3 + 1)}^{3}}{{(2 + √3)}^{3}} }$

$\large\boxed{\textbf{= \cfrac{8 + 3√3 + 1}{8 + 3√3} }}$

$\LARGE\textbf{\underline{\underline{Here :-}}}$

• $\large\textbf{ {2}^{3} = 8 }$

• $\large\textbf{ {√3}^{3} = √3 × 3 × 3 = 3√3 }$