Question

If $x=\sqrt{6}+\sqrt{5}$,then $x^2+\frac{1}{x^2}-2=$ ?

• A. $2\sqrt{6}$
• B. $2\sqrt{5}$
• C. $24$
• D. $20$

Answer 1

The correct option is D $20$

$x=\sqrt{6}+\sqrt{5}$
$\frac{1}{x}=\frac{1}{\sqrt{6}+\sqrt{5}}=\frac{\sqrt{6}-\sqrt{5}}{6-5}$
$\frac{1}{x}=\sqrt{6}-\sqrt{5}$
$x-\frac{1}{x}=2\sqrt{5}$
Squaring both sides:
$x^2+\frac{1}{x^2}-2=(2\sqrt{5}{)}^2=20$