Question

please help...........

Answer 1

$x + \frac{1}{x} = 4$

Squaring both sides ,
${x}^{2} + { \frac{1}{ {x}^{2} } } + 2 \times x \times \frac{1}{x} = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2= 14 - 2 \\ \\ (x - \frac{1}{x} ) {}^{2} = 12 \\ \\ x - \frac{1}{x} = 2 \sqrt{3}$
Cubing both sides ,

${x}^{3} - \frac{1}{ {x}^{3} } - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) = 24 \sqrt{3} \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = 30 \sqrt{3} \: \: \: \: \: \: Ans.$

Answer 2

the answer is above hope it will help you