If $x - \dfrac{1}{x} = 3$, find $x^{2} + \dfrac{1}{x^{2}}$.

If $x - \dfrac{1}{x} = 3$, find $x^{2} + \dfrac{1}{x^{2}}$.
  1. $11$
  2. $9$
  3. $7$
  4. $13$

Solution

$\left(x - \dfrac{1}{x}\right)^{2} = x^{2} - 2 + \dfrac{1}{x^{2}} = 9 \Rightarrow x^{2} + \dfrac{1}{x^{2}} = 11$.

Asked in: IMO

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