If $a^{2} + b^{2} = 50$ and $a - b = 6$, find $ab$.

If $a^{2} + b^{2} = 50$ and $a - b = 6$, find $ab$.
  1. $7$
  2. $14$
  3. $22$
  4. $11$

Solution

$(a-b)^{2} = a^{2} + b^{2} - 2ab \Rightarrow 36 = 50 - 2ab \Rightarrow ab = 7$.

Asked in: IMO

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