Question

if x=3+2√2 then find (x-1/x)³​

Answer 1

Answer:

$x = 3 + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ \frac{1}{x} = \frac{3 - 2 \sqrt{2} }{9 - 8} = 3 - 2 \sqrt{2} \\ x - \frac{1}{x} = 4 \sqrt{2} \\ ( {x - \frac{1}{x} })^{3} = ( {4 \sqrt{2} })^{3} = 128 \sqrt{2}$