Question

x²+1/x²=51then find x³-1/x³​

Answer 1

Answer:

l 364 l

Explanation:

${(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ {x}^{ 3} - {y}^{3} = (x - y)( {x}^{2} + {y}^{2} + 2xy) \\ \\ given \\ \\ y = \frac{1}{x} \\ \\ (x - \frac{1}{x} ) {}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 49 \\ \\ x - \frac{1}{x} = |7| \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = (x - \frac{1}{x} )( {x}^{2} + \frac{1}{ {x}^{2} } + 1) \\ \\ = |7| (52) \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = |364| \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = 364 \\ \\ {x}^{3} - \frac{1}{ {x}^{3} } = - 364$

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Answer 2

Answer:

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