Question

if x power 4 + 1 / x power 4 = 119 , find x cube - 1 / x cube

Answer 1

${x}^{4} + \frac{1}{ {x}^{4} } = 119 \\ {( {x}^{2} + \frac{1}{ {x}^{2} } ) }^{2} - 2 = 119 \\ {x}^{2} + \frac{1}{ {x}^{2} } = \sqrt{121} = 11 \\ {(x - \frac{1}{x} )}^{2} + 2 = 11 \\ x - \frac{1}{x} = \sqrt{9} = + \: \: or \: \: - 3$
${x}^{3} - \frac{1}{ {x}^{3} } = {(x - \frac{1}{x} )}^{3} + 3(x - \frac{1}{x} ) \\ + \: \: or \: \: - 36$