Question

if (x+ 1/x)²=3 then find x³+1/x³ ​

Answer 1

Answer:

WE KNOW THAT -

${(x + \frac{1}{x} )}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} )$

SO,

${x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x}) }^{3} - 3(x + \frac{1}{x} )$

BUT -

$x + \frac{1}{x} = \sqrt{3}$

THEN –

${x}^{3} + \frac{1}{ {x}^{3} } = { (\sqrt{3} )}^{3} - 3 \sqrt{3}$

$= 3 \sqrt{3} - 3 \sqrt{3} = 0$

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