Question
Question: If a, b, c are non-zero real numbers such that 3(a<sup>2</sup> + b<sup>2</sup> + c<sup>2</sup> + 1)...
If a, b, c are non-zero real numbers such that
3(a2 + b2 + c2 + 1) = 2 (a + b + c + ab + bc + ca) then a, b, c are in –
A
A.P.only
B
G.P.only
C
A.P and G.P. only
D
A.P, G.P. and H.P.
Answer
A.P, G.P. and H.P.
Explanation
Solution
3(a2 + b2 + c2 + 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