Question

if x = 3+2√2 then find the value of[x-1/x]^3​

Answer 1

$\huge\underline\mathcal{Answer:-}$

$x = 3 + 2 \sqrt{2} \\ \frac{1}{x} = \frac{1}{3 + 2 \sqrt{2} } \\ = \frac{1}{3 + 2 \sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ = \frac{3 - 2 \sqrt{2} }{9 - 8} \\ = 3 - 2 \sqrt{2} \\ x - \frac{1}{x} = 3 + 2 \sqrt{2} - 3 + 2 \sqrt{2} \\ = 4 \sqrt{2} \\ => {4 \sqrt{2} }^{3} = 32$

$\huge\underline\mathcal{Answer=3\:2}$