If $a - b = 5$ and $ab = 14$, find $a^{2} + b^{2}$.

If $a - b = 5$ and $ab = 14$, find $a^{2} + b^{2}$.
  1. $53$
  2. $25$
  3. $39$
  4. $11$

Solution

$a^{2} + b^{2} = (a-b)^{2} + 2ab = 25 + 28 = 53$.

Asked in: IMO

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