Question

if x=3+2√2 find x-1/x

Answer 1

Answer:

4√2

Step-by-step explanation:

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

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

$x - \frac{1}{x} = (3 + 2 \sqrt{2} ) - (3 - 2 \sqrt{2} ) \\ = 3 - 3 + 2 \sqrt{2} + 2 \sqrt{2} = 4 \sqrt{2}$