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Question

Mathematics Question on Arithmetic Progression

If 3x22ax+(a2+2b2+2c2)=2(ab+bc),3x^2-2ax+(a^2+2b^2+2c^2) = 2(ab+bc), then a,b,c can be in

A

A.P

B

G.P

C

H.P

D

none of these

Answer

A.P

Explanation

Solution

The given result can be expressed as follows :
\left\\{x-(a-b)^2\right\\}+\left\\{x-(b-c)^2\right\\}+(x-c)^2=0
x=ab,x=bc,x=cx=a-b,x=b-c,x=c
ab=bc=ca-b=b-c=c
From ab=bc, 2b=a+ca-b=b-c,\ 2b=a+c
Therefore, a,b,ca,b,c can be in A.P.
So, the correct option is (A) : A.P.