If $a^{3} + b^{3} = 35$ and $a + b = 5$, find $ab$.

If $a^{3} + b^{3} = 35$ and $a + b = 5$, find $ab$.
  1. $6$
  2. $5$
  3. $7$
  4. $3$

Solution

$125 = 35 + 15ab \Rightarrow ab = 6$.

Asked in: IMO

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