Question

Solve this ques fast

Answer 1

$x = 3 - 2 \sqrt{2}$

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

${x}^{3} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x} )( {x}^{2} + x \times \frac{1}{x} + \frac{1}{ {x}^{2} } ) \\ \\ = (3 - 2 \sqrt{2} - 3 - 2 \sqrt{2} )( {x}^{2} + 1 + { \frac{1}{x} }^{2} ) \\ \\ = ( - 4 \sqrt{2} )(9 + 8 - 12 \sqrt{2} + 9 + 8 + 12 \sqrt{2 } + 1) \\ \\ = ( - 4 \sqrt{2} )(35) \\ \\ = - 140 \sqrt{2}$