Question

If x = 5√2 – 7, find the value of x^3 - 1/x^3​

Answer 1

$x = 5 \sqrt{2} - 7 \\ \\ \frac{1}{x} = \frac{1}{5 \sqrt{2} - 7 } \\ \frac{1}{x} = \frac{5 \sqrt{2} + 7}{50 - 49} \\ \frac{1}{x} = 5 \sqrt{2} + 7 \\ \\ x - \frac{1}{x} = 5 \sqrt{2} - 7 - 5 \sqrt{2} - 7 \\ = - 14 \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = ( {x - \frac{1}{x} })^{3} + 3(x - \frac{1}{x} ) \\ = ( { - 14})^{3} + 3( - 14) \\ = - 2744 - 52 \\ = - 2796$