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January 5th, 2017, 12:21 AM   #1
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algebraic expression

If $a(a-c)^2+b(b-a)^2+c(c-b)^2=0$ then prove that $a=b=c$
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January 5th, 2017, 12:50 AM   #2
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You would need additional information, such as being given that a, b, and c are real and non-negative.
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January 5th, 2017, 01:08 AM   #3
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here $a,b,c\geq 0$
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January 5th, 2017, 03:13 AM   #4
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That implies $a(a-c)^2=b(b-a)^2=c(c-b)^2=0$,
from which it's easy to show that $a = b = c$.
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