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Expert: - 10/1/2008


Question
Prove that for all real numbers a,b,and c that
bc+ac+ab (is less than or equal to) a^2+b^2+c^2

Answer
Questioner:   Pete
Category:  Advanced Math
Private:  No
 
Subject:  Mathematical Proofs
Question:  Prove that for all real numbers a,b,and c that
bc+ac+ab (is less than or equal to) a^2+b^2+c^2
............................................
Hi, Pete,
In the future, please tell me just what you are studying. What subject?  What part of it?

Consider the difference:

2(a^2 + b^2 + c^2) - 2(ab + ac + ab) =

2a^2 + 2b^2 + 2c^2 - 2ab - 2ac - 2ab =

a^2 - 2ab + b^2 + a^2 - 2ac + c^2 + b^2 - 2bc + c^2  =

(a - b)^2 + (a - c)^2 + (b - c)^2

And that, my friend is >= 0.

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