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January 5th, 2017, 12:21 AM  #1 
Senior Member Joined: Jul 2011 Posts: 392 Thanks: 15  algebraic expression
If $a(ac)^2+b(ba)^2+c(cb)^2=0$ then prove that $a=b=c$

January 5th, 2017, 12:50 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 17,177 Thanks: 1285 
You would need additional information, such as being given that a, b, and c are real and nonnegative.

January 5th, 2017, 01:08 AM  #3 
Senior Member Joined: Jul 2011 Posts: 392 Thanks: 15 
here $a,b,c\geq 0$

January 5th, 2017, 03:13 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,177 Thanks: 1285 
That implies $a(ac)^2=b(ba)^2=c(cb)^2=0$, from which it's easy to show that $a = b = c$. 

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algebraic, algebric, expression 
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