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138. If a2 + b2 + c2 – ab – bc – ca = 0, then
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- a = b = c
- a ≠ b = c
- a = b ≠ c
- a ≠ b ≠ c
- a = b = c
Correct Option: A
a2 + b2 + c2 – ab – bc – ca = 0
⇒ 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
It is possible only when,
a – b = 0 ⇒ a = b
b – c = 0 ⇒ b = c
c – a = 0 ⇒ c = a
∴ a = b = c
