$$\root 3 \of {{{\left( {333} \right)}^3} + {{\left( {333} \right)}^3} + {{\left( {334} \right)}^3} - 3 \times 333 \times 333 \times 334} $$ is equal to = ?
A. 12
B. 11
C. 10
D. 15
Answer: Option C
Solution(By Examveda Team)
According to question$$\root 3 \of {{{\left( {333} \right)}^3} + {{\left( {333} \right)}^3} + {{\left( {334} \right)}^3} - 3 \times 333 \times 333 \times 334} $$
As we know that
a3 + b3 + c3 - 3abc
= $$\frac{1}{2}$$ (a + b + c)[(a - b)2 + (b - c)2 + (c - a)2]
= $$\frac{1}{2}$$ (333 + 333 + 334)[(333 - 333)2 + (333 - 334)2 + (334 - 333)2]
= $$\frac{1}{2}$$ × 1000[0 + 1 + 1]
= $$\frac{1}{2}$$ × 1000 × 2
= $$\root 3 \of {1000} $$
= 10
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