-
(2.247)3 + (1.730)3 + (1.023)3 -3 x 2.247 x 1.730 x 1.023 / [(2.247)2 + (1.730)2 + (1.023)2 - 2.247 x 1.730 - 1.730 x 1.023 - 2.247 x 1.023] = ?
-
- 1.730
- 4
- 5
- 5.247
Correct Option: C
We know that, a3 + b3 + c3 - 3abc
= (a + b + c) (a2 + b2 + c2 - ab - bc - ca)
⇒ (a + b + c) = (a3 + b3 + c3 - 3abc/a2 + b2 + c2 - ab - bc - ca) ....(i)
Given that,
(2.247)3 + (1.730)3 + (1.023)3 - 3 x 2.247 x 1.730 x 1.023/ (2.247)2 + (1.730)2 + (1.023)2 - (2.247 x 1.730) - (1.730 x 1.023) - (2.247 x 1.023)
= 2.247 + 1.730 x 1.023) - (2.247 x 1.023)
= (2.247 + 1.730 + 1.023) [from Eq.(i)]
= 5.000 = 5
