$$\root 3 \of {{{\left( {333} \right)}^3} + {{\left( {333} \right)}^3} + {{\left( {334} \right)}^3} - 3 \times 333 \times 333 \times 334} $$           is equal to = ?

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