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 January 4th, 2017, 11:21 PM #1 Senior Member   Joined: Jul 2011 Posts: 395 Thanks: 15 algebraic expression If $a(a-c)^2+b(b-a)^2+c(c-b)^2=0$ then prove that $a=b=c$
 January 4th, 2017, 11:50 PM #2 Global Moderator   Joined: Dec 2006 Posts: 18,048 Thanks: 1395 You would need additional information, such as being given that a, b, and c are real and non-negative.
 January 5th, 2017, 12:08 AM #3 Senior Member   Joined: Jul 2011 Posts: 395 Thanks: 15 here $a,b,c\geq 0$
 January 5th, 2017, 02:13 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,048 Thanks: 1395 That implies $a(a-c)^2=b(b-a)^2=c(c-b)^2=0$, from which it's easy to show that $a = b = c$. Thanks from panky

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