Question

if (x+1/x)²=3 then what is x³+1/x³​

Answer 1

Answer:

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Answer 2

$\: \: \: \: \: \: \: \: {(x + \frac{1}{x} )}^{2} = 3 \\ = > (x + \frac{1}{x} ) = \sqrt{3}$

Now,

$\: \: \: \: \: \: \: \: \: \: \: \: ( {x + \frac{1}{x}) }^{3} = {(\sqrt{3} )}^{3} \\ \\ = = > {x}^{3} + \frac{1}{ {x}^{3} } + 3x. \frac{1}{x} (x + \frac{1}{x} ) = 3 \sqrt{3} \\ \\ = = > {x}^{3} + \frac{1}{ {x}^{3} } + 3 \sqrt{3} = 3 \sqrt{3} \\ \\ = = > {x}^{3} + \frac{1}{ {x}^{3} } = 3 \sqrt{3} - 3 \sqrt{3 } \\ \\ = = > {x}^{3} + \frac{1}{ {x}^{3} } = 0$