Question

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Answer 1

$\huge{ \underline{ \text{Given}}}$

• $\sf{ \large{x - \frac{1}{x} = 3}}$

$\huge{ \underline{ \text{To \: find}}}$

• $\large{ \sf{x {}^{3} - \frac{1}{x {}^{3} } = }}$

$\huge{ \underline{ \underline{ \text{✤Solution}}}}$

$\large{ \sf{x {}^{3} - \frac{1}{x {}^{3} } }}$

$\sf{ \large{ = > (x) {}^{3} - ( \frac{1}{x} ) {}^{3} }}$

$\sf{ \large{ = > (x - \frac{1}{x} ) {}^{3} + 3 \times x \times \frac{1}{x} (x - \frac{1}{x} )}}$

$\sf{ \large{ = > ( - 3) {}^{3} + 3 \times ( - 3)}}$

$\sf{ \large{ = > - 27 + 3( - 3)}}$

$\sf{ \large{ = > - 27 + ( - 9)}}$

$\sf{ \large{ = > - 27 - 9}}$

$\sf{ \large{ \boxed{ \orange{ = > - 36}}}}$

$\sf{ \underline{hence \: the \: value \: of \: {x}^{3} - \frac{1}{ {x}^{3} } = - 36}}$

Important Formulas:-

$\sf{ \bold{ {a}^{3} - {b}^{3} = (a - b) {}^{3} + 3ab(a - b)}}$

$\sf{ \bold{ {a}^{3} - {b}^{3} = (a + b) {}^{3} - 3ab(a + b)}}$

❖Hope this helps you!!

Answer 2

Answer:

-36 is your required answer

Step-by-step explanation:

hope it helps you