If $a + b = 5$ and $a^{2} - ab + b^{2} = 7$, find $a^{3} + b^{3}$.

If $a + b = 5$ and $a^{2} - ab + b^{2} = 7$, find $a^{3} + b^{3}$.
  1. $35$
  2. $12$
  3. $25$
  4. $45$

Solution

$a^{3} + b^{3} = (a+b)(a^{2}-ab+b^{2}) = 5 \cdot 7 = 35$.

Asked in: IMO

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