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$a+\frac1a=\sqrt3$ হলে, $a^2+\frac{1}{a^2}$ এর মান কত?

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$a+\frac1a=\sqrt3$ হলে, $a^2+\frac{1}{a^2}$ এর মান কত?

অথবা,

$a+\frac1a=\sqrt3$ হলে, $a^2+\left(\frac1a\right)^2$ এর মান কত?

Options :

  • (A) $6$
  • (B) $4$
  • (C) $2$
  • (D) $1$

1 Answer

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$a^2+\frac1{a^2}=\left(a\right)^2+\left(\frac1{a^2}\right)$

= $\left(a+\frac1a\right)^2-2.a.\frac1a$

= $\left(\sqrt3\right)^2-2$

= $3-2$

= $1$

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