Question

If x=2+√3 find (x+1/x)^3

Answer 1

$\large\sf\underline{Given}$

• $\sf\:x=2+\sqrt{3}$

$\large\sf\underline{To\:find}$

• $\sf\:(x+\frac{1}{x})^{3}$

$\large\sf\underline{Solution}$

As x = $\sf\:2+\sqrt{3}$

So $\sf\:\frac{1}{x}=2-\sqrt{3}$

Therefore :

$\sf\:(x+\frac{1}{x})$

$\sf➙\:2+\sqrt{3}+2-\sqrt{3}$

$\sf➙\:2+2+\sqrt{3}-\sqrt{3}$

${\sf{{\pink{➙\:4}}}}$

Now substituting the value of $\sf\:(x+\frac{1}{x})$ in $\sf\:(x+\frac{1}{x})^{3}$

We get :

$\sf\:(x+\frac{1}{x})^{3}$

$\sf➙\:4^{3}$

${\sf{{\pink{➙\:64}}}}$

• Thnku :)