Question

x2+1/x2=83findx3-1/x3

Answer 1

.........................

Answer 2

${x}^{2} + \frac{1}{ {x}^{2} } = 83 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2x \frac{1}{x} = 83 - 2 \\ {(x - \frac{1}{x}) }^{2} = 81 \\ x - \frac{1}{x} = + - 9 \\ ( {x}^{3} - \frac{1}{ {x}^{3} } ) = (x - \frac{1 }{x} )( {x}^{2} + \frac{1}{ {x}^{2} } + 1) \\ = + - 9(83 + 1) = + - 756$