If X 2 + 1 X 2 = 18 ; Find : X 3 − 1 X 3 - Mathematics

If $x^{2} + \frac{1}{x^{2}} = 18$ ; find : $x^{3} - \frac{1}{x^{3}}$

बेरीज

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

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

⇒ 64 = $x^{3} - \frac{1}{x^{3}} - 3 (4)$

⇒ $x^{3} - \frac{1}{x^{3}}$
= 64 + 12
= 76.

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