Question

If x = 5√2 − 7,find the value ofx3-1/x3

Answer 1

Answer:

x3-1/x3

(5✓2-7)3-1/(5✓2-7)3

15✓2-21-1/15✓2-21

15✓2-22/15✓2-21

Answer 2

$x = 5 \sqrt{2} - 7 \\ \frac{1}{x} = \frac{1}{5 \sqrt{2} - 7 } \times \frac{5 \sqrt{2} + 7 }{5 \sqrt{2} + 7} \\ \frac{1}{x} = \frac{5 \sqrt{2} + 7}{50 - 49} \\ \frac{1}{x} = 5 \sqrt{2} + 7 \\ \\ x - \frac{1}{x} = 5 \sqrt{2} - 7 - 5 \sqrt{2} - 7 \\ = - 14 \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = ( {x - \frac{1}{x} })^{3} + 3(x - \frac{1}{x} ) \\ = ( - 14) ^{3} + 3 \times ( - 14) \\ = - 2744 - 42 \\ = - 2786$