Question

If x=3−2√2, find the value of i) x−1/X

Answer 1

$x \: = 3 - 2 \sqrt{2}$

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

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{ {3}^{2} - ( 2\sqrt{2}) ^{2} }$

$\frac{1}{x} = \frac{3 + 2 \sqrt{2} }{9 -8}$

$\frac{1}{x} = 3 + 2 \sqrt{2}$

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

$x - \frac{1}{x} = - 4 \sqrt{2}$