If $a = 2,\ b = 3,\ c = -5$ (so $a + b + c = 0$), then $a^{3} + b^{3} + c^{3}$ equals

If $a = 2,\ b = 3,\ c = -5$ (so $a + b + c = 0$), then $a^{3} + b^{3} + c^{3}$ equals
  1. $-90$
  2. $90$
  3. $0$
  4. $30$

Solution

$3abc = 3 \cdot 2 \cdot 3 \cdot (-5) = -90$. Check: $8 + 27 - 125 = -90$.

Asked in: IMO

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