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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 b)G.P c)both a and b d) none of these Pls give the solution for this question [A2=a square and so on other two]

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
b)G.P
c)both a and b
d) none of these
 
 
 
 
Pls give the solution  for this question
[A2=a square and so on other two]
 
 
 

Grade:12th pass

3 Answers

Arun
25750 Points
5 years ago
 
Dear student 
 
a^2 + b^2 + c^2 + 1 = 2/3
 
a^2 + b^2 + c^2 = – 1/3
 
this can never happen as addition of some squares can never be negative
 
hence a,b , c are not real numbers
Aditya Gupta
2081 Points
5 years ago
The above question is merely tricky.
Note that the above equation can be written as 
(a-b)^2+(b-c)^2+(c-a)^2+(a-1)^2+(b-1)^2+(c-1)^2=0
So a=b=c=1
Hence a,b,c are in both AP and GP
Arun
25750 Points
5 years ago
Oh sorry man
 
I thought that the expression in second line is discrete.
There is a silly mistake from my side in reading the question as expressions are written in diffrenet line

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