Question

if x²+1/x=18,find the value of x³-1/x³.can someone solve this question.

Answer 1

$here \: is \: ur \:ans \: dear \: friend$
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$(x - \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2x \frac{1}{x } \\ (x - \frac{1}{x} ) {}^{2} = 18 - 2 \\ (x - \frac{1}{x} ) {}^{2} = 16 \\ (x - \frac{1}{x} ) = \sqrt{16} = 4 \\ \\ (x - \frac{1}{x} ) {}^{3} = {x}^{3} - \frac{1}{ {x}^{3} } - 3x \frac{1}{x} (x - \frac{1}{x}) \\ {4}^{3 } = {x}^{3} - \frac{1}{ {x}^{3} } - 3 \times 4 \\ {x}^{3} - \frac{1}{ {x}^{3} } = 64 + 12 \\ {x}^{3} - \frac{1}{ {x}^{3} } = 76 \: ans$