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$x-\frac1x=1$ হলে $x^3-\frac{1}{x^3}$ এর মান কত?

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$x-\frac1x=1$ হলে $x^3-\frac{1}{x^3}$ এর মান কত?

অথবা,

$x-\frac1x=1$ হলে $x^3+\left(\frac1x\right)^3$ এর মান কত?

Options :

  • (A) $1$
  • (B) $2$
  • (C) $3$
  • (D) $4$

1 Answer

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Best answer

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

= $\left(x-\frac1x\right)^3+3.x.\frac1x.\left(x-\frac1x\right)$

= $1+3 \times 1$ [ মান বসিয়ে ]

= $4$

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