If x + y + z = 6, then the value of (x - 1)3 + (y - 2)3 + (z - 3)3 is?
A. 3(x - 1)(y + 2)(z - 3)
B. 3(x + 1)(y - 2)(z - 3)
C. 3(x - 1)(y - 2)(z + 3)
D. 3(x - 1)(y - 2)(z - 3)
Answer: Option D
Solution (By Examveda Team)
$$\eqalign{ & x + y + z = 6 \cr & {\left( {x - 1} \right)^3}{\text{ + }}{\left( {y - 2} \right)^3}{\text{ + }}{\left( {z - 3} \right)^3} \cr & \therefore {\text{As, }}x + y + z = 6 \cr & {\text{Take values}} \cr & x = 1 \cr & y = 2 \cr & z = 3 \cr & \left( {1 + 2 + 3} \right) = 6 \cr & \therefore {\left( {1 - 1} \right)^3}{\text{ + }}{\left( {2 - 2} \right)^3}{\text{ + }}{\left( {3 - 3} \right)^3} \cr & = 0 \cr} $$Now assume values in options.
Option 'D' satisfies the given relation.
Hence 'D' is correct.
This Question Belongs to Arithmetic Ability >> Algebra
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