If x = 332, y = 333, z = 335, then the value of x3 + y3 + z3 - 3xyz is?
A. 7000
B. 8000
C. 9000
D. 10000
Answer: Option A
Solution(By Examveda Team)
Here, x = 332, y = 333, z = 335Find x3 + y3 + z3 - 3xyz
$$ = \frac{1}{2}\left( {x + y + z} \right)$$ $$\left[ {{{\left( {x - y} \right)}^2} + {{\left( {y - z} \right)}^2} + {{\left( {z - x} \right)}^2}} \right]$$
$$ = \left( {\frac{{332 + 333 + 335}}{2}} \right)$$ $$\left[ {{{\left( {332 - 333} \right)}^2} + {{\left( {333 - 335} \right)}^2} + {{\left( {332 - 335} \right)}^2}} \right]$$
$$\eqalign{ & = \frac{{1000}}{2}\left[ {{1^2} + {2^2} + {3^2}} \right] \cr & = \frac{{1000}}{2}\left( {14} \right) \cr & = 7000{\text{ }} \cr} $$
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