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April 21st, 2011, 11:56 PM  #1 
Member Joined: Feb 2009 Posts: 54 Thanks: 0  Can't simplify
When I type I get as an answer. Yet I can't simplify it on paper. Either I get many pages of transformations and come back to the start or I go far away into the wrong weird big answers. I tried to multiply and then multiply denominator by until roots in it disappear but I come back to the start like I said above. Looks like I'm walking in circles. This is a part of a bigger polynomial which my calculator can solve but I can't. There must be some trick my calculator knows but I don't. 
April 22nd, 2011, 12:04 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Can't simplify
We have: We need to rewrite the first radicand: This allows us to write: 
April 22nd, 2011, 12:18 AM  #3 
Member Joined: Feb 2009 Posts: 54 Thanks: 0  Re: Can't simplify
Okay that was surprising. And that calculator can do that 
April 22nd, 2011, 12:27 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Can't simplify
What was essential was the recognition that 5 + 2 = 7 and 5·2 = 10. If you have: and d + e = a and d·e = c then 

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