Question

If $x=3+2\sqrt{2}$. Then find the value of $x+\frac{1}{x}$

Answer 1

Given $3-2\sqrt{2}$
Given eq $x+\frac{1}{x}=\frac{x^2+1}{x}$ ...1
now put the value of x in eq 1
$\Rightarrow \frac{{(3-2\sqrt{2})}^2+1}{3-2\sqrt{2}}$
$\Rightarrow \frac{9-12\sqrt{2}+8+1}{3-2\sqrt{2}}$
$\Rightarrow \frac{18-12\sqrt{2}}{3-2\sqrt{2}}$
$\Rightarrow \frac{6(3-2\sqrt{2})}{3-2\sqrt{2}}=6$