-
If a + b + c = 0, then
2a2 + 2b2 + 2c2 + 3 = ? b2 + c2 − a2 c2 + a2 − b2 a2 + b2 − c2
-
- 3
- – 4
- 0
- – 3
Correct Option: C
If a + b + c = 0
a + b = – c
On squaring both sides,
⇒ a2 + b2 + 2ab = c2
Similarly,
a2 = b2 + c2 + 2ac
b2 = a2 + c2 + 2ac
| ∴ Expression = | + | + | + 3 | |||
| b2 + c2 − a2 | c2 + a2 − b2 | a2 + b2 − c2 |
| L.H.S. = | + 1 + | + 1 + | + 1 | |||
| b2 + c2 − a2 | c2 + a2 − b2 | a2 + b2 − c2 |
| L.H.S. = | + 1 + | + 1 + | + 1 | |||
| b2 + c2 − a2 | c2 + a2 − b2 | a2 + b2 − c2 |
| = | + | + | = (a2 + b2 + c2) | |||
| b2 + c2 − a2 | c2 + a2 − b2 | a2 + b2 − c2 |
 | + | + |  | |||
| b2 + c2 − b2 − c2 − 2bc | c2 + a2 − c2 − a2 − 2ac | a2 + b2 − a2 − b2 − 2ab |
| = (a2 + b2 + c2) |  | − | − |  | |||
| −2bc | 2ac | 2ab |
| = (a2 + b2 + c2) | | | = 0 | |
| −2abc |
