Question
If x + y = 15, then the value of (x - 10)3 + (y - 5)3 is?
Answer: Option D
$$\eqalign{
& x + y = 15 \cr
& \Rightarrow x - 10 = 5 - y \cr
& \Rightarrow x - 10 = - \left( {y - 5} \right) \cr
& {\text{Take cube on both sides}} \cr
& \Rightarrow {\left( {x - 10} \right)^3} = - {\left( {y - 5} \right)^3} \cr
& \Rightarrow {\left( {x - 10} \right)^3} + {\left( {y - 5} \right)^3} = 0 \cr} $$
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$$\eqalign{
& x + y = 15 \cr
& \Rightarrow x - 10 = 5 - y \cr
& \Rightarrow x - 10 = - \left( {y - 5} \right) \cr
& {\text{Take cube on both sides}} \cr
& \Rightarrow {\left( {x - 10} \right)^3} = - {\left( {y - 5} \right)^3} \cr
& \Rightarrow {\left( {x - 10} \right)^3} + {\left( {y - 5} \right)^3} = 0 \cr} $$
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