-
3√(333)3 + (333)3 + (334)3 − 3 × 333 × 333 × 334 is equal to
-
- 12
- 11
- 10
- 15
Correct Option: C
We know that
a3 + b3 + c3 – 3abc
= (a+b+c ) (a2 + b2 + c2 – ab – bc – ca)
| = | (a + b + c)[(a – b)2 + (b – c)2 + (c – a)2] | |
| 2 |
∴ 3√(333)3 + (333)3 + (334)3 − 3 × 333 × 333 × 334
= 3√(1/2)(333 + 333 + 334) [(333 − 333)2 + (333 − 334)2 + (334 − 333)2]
= 3√(1/2) × 1000 × 2
= 3√1000
= 3√10 × 10 × 10
= 10
