If x + y = 15, then the value of (x - 10)³ + (y - 5)³ is?

Solution (By Examveda Team)

$$\eqalign{ & x + y = 15 \cr & \Rightarrow x - 10 = 5 - y \cr & \Rightarrow x - 10 = - \left( {y - 5} \right) \cr & {\text{Take cube on both sides}} \cr & \Rightarrow {\left( {x - 10} \right)^3} = - {\left( {y - 5} \right)^3} \cr & \Rightarrow {\left( {x - 10} \right)^3} + {\left( {y - 5} \right)^3} = 0 \cr} $$