Question

if X=3+2√2 then find the value of ( x- 1/X)cube

Answer 1

solution:-


given by:-


$x = 3 + 2 \sqrt{2} \\ (x - \frac{1}{x} ) \\ 3 + 2 \sqrt{2} - \frac{1}{3 + 2 \sqrt{2} } \\ \frac{9 + 6 \sqrt{2} + 6 \sqrt{2 } + 8 - 1 }{3 + 2 \sqrt{2} } \\ \frac{16 + 12 \sqrt{2} }{3 + 2 \sqrt{2} } \\ \frac{16 + 12 \sqrt{2} }{3 + 2\sqrt{2} } \times \frac{3 - 2 \sqrt{2} }{3 - 2 \sqrt{2} } \\ \frac{48 + 36 \sqrt{2} - 32 \sqrt{2} - 48 }{9 - 8} \\ 4 \sqrt{2} ans$