-
If a + b + c = 0, then the value of (a + b – c)2 + (b + c – a)2 + (c + a – b)2 is
-
- 0
- 8abc
- 4(a2 + b2 + c2)
- 4 (ab + bc + ca)
- 0
Correct Option: C
a + b + c = 0 (Given)
∴ a + b = – c
b + c = – a
c + a = – b
∴ (a + b – c)2 + (b + c – a)2 + (c + a – b)2 = (-c – c)2 + (-a – a)2 + (-b – b)2
= (– 2c)2 + (- 2a)2 + (– 2b)2 = 4c2 + 4a2 + 4b2 = 4(c2 + a2 + b2)
