If $a + b = 10$ and $a^{2} + b^{2} = 58$, find $ab$.

If $a + b = 10$ and $a^{2} + b^{2} = 58$, find $ab$.
  1. $21$
  2. $29$
  3. $42$
  4. $58$

Solution

$(a+b)^{2} = a^{2} + b^{2} + 2ab \Rightarrow 100 = 58 + 2ab \Rightarrow ab = 21$.

Asked in: IMO

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