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March 16th, 2016, 05:22 PM  #1 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0  Don't use the rational root theorem to solve the following:
Given the following problem, how might one go about solving this without a calculator and without using the rational root theorem: The sum of the solutions of $\displaystyle (x^23x)^2  (3x^2  9x)=4$ is: 
March 16th, 2016, 05:38 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,931 Thanks: 1125 Math Focus: Elementary mathematics and beyond 
Using the substitution $u=x^23x$, that equation simplifies to $u^23u4=0$. Can you solve it now?

March 16th, 2016, 06:00 PM  #3 
Senior Member Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 
I certainly can! Why do I never think of this stuff? It's frustrating how easy I overlook simple things like that. Thanks.

March 16th, 2016, 06:03 PM  #4 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,790 Thanks: 629 Math Focus: Yet to find out.  

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