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If a2 + b2 + c2 = ab + bc + ca, where a, b, c are non zero real numbers,
then the value of a + b is c
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- 2
- 1
- 0
- –1
Correct Option: A
a2 + b2 + c2 = ab + bc + ca
⇒ 2a2 + 2b2 + 2c2 = 2ab + 2bc + 2ca
⇒ a2 – 2ab + b2 + b2 – 2bc + c2 + c2 – 2ac + a2 = 0
⇒ (a – b)2 + (b – c)2 + (c – a)2 = 0
∴ a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c
| ∴ | = | = 2 | ||
| c | a |
