Find the value of equation

If a + b + c = 0, then the value of (a + b – c)2 + (b + c – a)2 + (c + a – b)2 is

  1. 0
  2. 8 abc
  3. 4(a2+b2+c2)
  4. 4(ab+bc+ca)
Manish Listener Asked on 17th July 2015 in Maths.
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1 Answer(s)

Answer: (1) 0
Explanation:-
Given-
a + b + c = 0
Then, a = – (b + c) ,    b = – (a + c)   &  c = – (a + b)
Then,
= (a + b + c)2 + (b + c – a)2 + (c + a – b)2
 Put the value of a, b & c
Then, (a + b – a – b )2 + (b + c – b – c)2 + (c + a – c – a )2
 = (0)2 + (0)2 + (0)2  = 0
Hence, the answer is (1) 0

Anurag Mishra Professor Answered on 17th July 2015.
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