If $(a-b)^{2} = 49$ and $ab = 6$, find $a^{2} + b^{2}$.

If $(a-b)^{2} = 49$ and $ab = 6$, find $a^{2} + b^{2}$.
  1. $61$
  2. $37$
  3. $55$
  4. $43$

Solution

$a^{2} + b^{2} = (a-b)^{2} + 2ab = 49 + 12 = 61$.

Asked in: IMO

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