Question

If x= 3+2√2 then find x-1/2

Answer 1

$x = 3 + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ = \frac{3 - 2 \sqrt{2} }{9 - 8} \\ = 3 - 2 \sqrt{2} \\ x - \frac{1}{x} = 3 + 2 \sqrt{2} - 3 + 2 \sqrt{2} \\ = 4\sqrt{2}$