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$x-\frac1x=p$ হলে, $x^3-\frac{1}{x^3}$ এর মান নির্ণয় কর।

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দেওয়া আছে,

$x-\frac{1}{x}=p$

বা, $\left(x-\frac{1}{x}\right)^3=\left(p\right)^3$
[ উভয় পার্শ্বে ঘন করে ]

বা, $x^3-\frac{1}{x^3}-3\cdot x\cdot\frac{1}{x}\left(x-\frac{1}{x}\right)=p^3$

বা, $x^3-\frac{1}{x^3}-3\cdot p=p^3$
[ মান বসিয়ে ]

$\therefore a^3-\frac{1}{a^3}=p^3+3p$ [Showed]

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