Question

Q.1.If x=3 + 2√2 then find the value of( − 1 )​

Answer 1

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