Question

x-1\x=3
find x³-1/x³​

Answer 1

$\mathrm{\underline{ \huge{Solution-}}}$

$\mathrm{Given - \left\{{x - \frac{1}{x} = 3}\right.}$

$\mathrm{To \: find - \left\{{ {x}^{3} - \frac{1}{ {x}^{3} } = }\right.}$

Let's solve the problem

we have,

$\mathrm{x - \frac{1}{x} = 3}$

Cubing on both sides, using algebraic Identity (a-b)³ = a³-b³-3ab(a-b) we get,

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

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } - 3( \cancel{x}) \bigg( \frac{1}{ \cancel{x}} \bigg) \bigg(x - \frac{1}{x} \bigg)} = 27$

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } - 3\bigg(x - \frac{1}{x} \bigg)} = 27$

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } - 3}(3) = 27$

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } - 9 = 27}$

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } = 27 + 9 }$

$⟹ \mathrm{ {x}^{3} - \frac{1}{ {x}^{3} } = 36}$

$\mathrm{ \underline{Answer - }Hence, the \: value \: of \: {x}^{3} - \frac{1}{ {x}^{3} } \: is \: 36. }$

Used formulae:-

• (a-b)³ = a³-b³-3ab(a-b)

:)