If $a + \dfrac{1}{a} = 6$, find $a^{2} + \dfrac{1}{a^{2}}$.

If $a + \dfrac{1}{a} = 6$, find $a^{2} + \dfrac{1}{a^{2}}$.
  1. $34$
  2. $36$
  3. $32$
  4. $38$

Solution

$\left(a+\dfrac{1}{a}\right)^{2} = a^{2} + 2 + \dfrac{1}{a^{2}} = 36 \Rightarrow a^{2} + \dfrac{1}{a^{2}} = 34$.

Asked in: IMO

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