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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]

one year ago

Arun
23491 Points

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
one year ago
1815 Points

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
one year ago
Arun
23491 Points

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
one year ago
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### Course Features

• 101 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions