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For real a, b, c if a2 + b2 + c2 = ab + bc + ca, the value of a + c is b
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- 3
- 1
- 2
- 0
Correct Option: C
a2 + b2 + c2 = ab + bc + ca
⇒ 2a2 + 2b2 + 2c2 – 2ab – 2bc – 2ca = 0
⇒ a2 + b2 – 2ab + b2 + c2 – 2bc + c2 + a2 – 2ca = 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 | ||
| b | a |
