Question

if x^2+1/x^2=51 find x^3-1/x^3

Answer 1

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$= > \bf {x}^{2} + \frac{1}{ {x}^{2} } =51 \\ \\ or. \: \: {x}^{2} + \frac{1}{ {x}^{2} } - 2x. \frac{1}{x} = 51 - 2x. \frac{1}{x} \\ \\ or. \: \: {(x - \frac{1}{x}) }^{2} = 51 - 2 = 49 \\ \\ or. \: \: x - \frac{1}{x} = \sqrt{49} = 7 \\ \\ now... \\ \\ = > \bf \: {x}^{3} - \frac{1}{ {x}^{3} } \\ \\ = (x - \frac{1}{x} )( {x}^{2} + \frac{1}{ { {x} }^{2} } + x. \frac{1}{x} ) \\ \\ = 7(51 + 1) = 7 \times 52 \\ \\ \bf \: = 364$
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Answer 2

Step-by-step explanation:

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