Question

if x2 +1/x2 = 27 then find the value of x3 - 1/x3​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ \\ \\ {(x + \frac{1}{ x } )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + \frac{2x}{x} \\ \\ {(x + \frac{1}{ x } )}^{2} = 27 + 2 \\ \\ x + \frac{1}{x} = \sqrt{29} \\ \\ ({x}^{2} + \frac{1}{ {x}^{2} }) \times (x + \frac{1}{x} ) = 27 \times \sqrt{29} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + \frac{x}{ {x}^{2} } + \frac{ {x}^{2} }{x} = 145.4 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + \frac{1}{x} + x = 145.4 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } + \sqrt{29} = 145.4 \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 145.4 - \sqrt{29} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 140$

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