If $a + b = 9$ and $a - b = 5$, find $ab$.

If $a + b = 9$ and $a - b = 5$, find $ab$.
  1. $14$
  2. $28$
  3. $11$
  4. $45$

Solution

Use $4ab = (a+b)^{2} - (a-b)^{2} = 81 - 25 = 56$. So $ab = 14$.

Asked in: IMO

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