Question

State True or False.

If $x=3-2\sqrt{2}$, then the value of $x-\frac{1}{x}$$=-4\sqrt{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

$x=3-2\sqrt{2}x-\frac{1}{x}=3-2\sqrt{2}-\frac{1}{3-2\sqrt{2}}=\frac{{(3-2\sqrt{2})}^2-1}{(3-2\sqrt{2})}=\frac{9+8-12\sqrt{2}-1}{3-2\sqrt{2}}=\frac{16-12\sqrt{2}}{3-2\sqrt{2}}rationalizethedenominator,\frac{(3+2\sqrt{2})(16-12\sqrt{2})}{(3-2\sqrt{2})(3+2\sqrt{2})}=\frac{48-36\sqrt{2}+32\sqrt{2}-48}{9-8}=-4\sqrt{2}$