Question

If x square + 1/x square=1 then tha value of x cube + 1/ x cube is:

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 1 \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ {(x + \frac{1}{x} )}^{2} = 3 \\ x + \frac{1}{x} = \sqrt{3}$
Now
${(x + \frac{1}{x}) }^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times x \times \frac{1}{x} (x + \frac{1}{x} ) \\ {( \sqrt{3} )}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3( \sqrt{3} ) \\ {x}^{3} + \frac{1}{ {x}^{3} } = {3}^{ \frac{3}{2} } - 3 \sqrt{3} \\ = 0$