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April 21st, 2011, 11:56 PM   #1
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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.
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April 22nd, 2011, 12:04 AM   #2
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Re: Can't simplify

We have:



We need to rewrite the first radicand:



This allows us to write:

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April 22nd, 2011, 12:18 AM   #3
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Re: Can't simplify

Okay that was surprising. And that calculator can do that
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April 22nd, 2011, 12:27 AM   #4
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Re: Can't simplify

What was essential was the recognition that 5 + 2 = 7 and 52 = 10.

If you have:

and d + e = a and de = c then

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