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CGP EDU Academic Team
Published on: August 13, 2026
If a, b, c are non-zero real numbers such that 3(a 2 + b 2 + c 2 + 1) = 2 (a + b + c + ab + bc + ca) then a, b, c are in –
Text Solution
Verified by ExpertsThe correct answer is:
D
3(a 2 + b 2 + c 2 + 1) – 2 (a + b + c + ab + bc + ca) = 0
⇒ [(a – b) 2 + (b – c) 2 + (c – a) 2 ]
+ [(a –1) 2 + (b –1) 2 + (c –1) 2 ] = 0
⇒ a – b = b – c = c – a = a –1 = b – 1 = c –1 = 0
⇒ a = b = c = 1 ⇒ AP, GP and HP
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