Question

State True or False.
If $x=3-2\sqrt{2}$, then the value of $x^2-\frac{1}{x^2}$$=-24\sqrt{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

$x=3-2\sqrt{2}$
$x^2-\frac{1}{x^2}={(3-2\sqrt{2})}^2-\frac{1}{{(3-2\sqrt{2})}^2}$
$\Rightarrow {(3-2\sqrt{2})}^2-\frac{1}{{(3-2\sqrt{2})}^2}\times \frac{{(3+2\sqrt{2})}^2}{{(3+2\sqrt{2})}^2}$
$\Rightarrow {(3-2\sqrt{2})}^2-\frac{{(3+2\sqrt{2})}^2}{({\left(3\right)}^2-{\left(2\sqrt{2}\right)}^2)}$
$\Rightarrow {(3-2\sqrt{2})}^2-\frac{{(3+2\sqrt{2})}^2}{{(9-8)}^2}$
$\Rightarrow {(3-2\sqrt{2})}^2-{(3+2\sqrt{2})}^2$
$\Rightarrow (17-12\sqrt{2})-(17+12\sqrt{2})$
$\Rightarrow 17-12\sqrt{2}-17-12\sqrt{2}$
$\Rightarrow -24\sqrt{2}$