If $a + b = 7$ and $ab = 12$, find $a^{2} + b^{2}$.

If $a + b = 7$ and $ab = 12$, find $a^{2} + b^{2}$.
  1. $25$
  2. $37$
  3. $13$
  4. $49$

Solution

$a^{2} + b^{2} = (a+b)^{2} - 2ab = 49 - 24 = 25$.

Asked in: IMO

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