Find the value of $\left(x + \dfrac{2}{x}\right)^{2}$ when $x = 3$.

Find the value of $\left(x + \dfrac{2}{x}\right)^{2}$ when $x = 3$.
  1. $\dfrac{121}{9}$
  2. $\dfrac{120}{9}$
  3. $\dfrac{49}{9}$
  4. $\dfrac{100}{9}$

Solution

At $x = 3$: $x + \dfrac{2}{x} = 3 + \dfrac{2}{3} = \dfrac{11}{3}$. Square: $\dfrac{121}{9}$.

Asked in: IMO

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