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## Problem with quartic

I just received and installed Maple 11.  (Maplesoft wouldn't sell me the student version, but I learned they have an unadvertised Home User version which is reasonable.  You have to call on the phone to order it.)  So far it's working well, but I can't figure out how to get an exact (symbolic) solution to a quartic with integer coefficients.

As a way of getting started, I tried having Maple give me an exact solution to the old "ladders across the alley" problem.  (E.g., ladders 40' and 30' long lean across an alley in opposite directions, crossing 10' above the ground.  How wide is the alley?)  Here is what I was able to get from Maple:

> solve(1/(40^2-x^2)^(1/2)+1/(30^2-x^2)^(1/2) = 1/10);
(1/2)
/     4           3                 2                                                  \
-10 RootOf\_Z  - 46 _Z  + 763 _Z  - 5374 _Z + 13585, index = 1/     ,

(1/2)
/     4            3                2                                                   \
10 RootOf\_Z  - 46 _Z  + 763 _Z  - 5374 _Z + 13585, index = 1/

> evalf([%]);
[-26.03287754, 26.03287754]

For the root of the quartic, instead of the RootOf expression, I was expecting to see the actual root,

23/2-(1/6)*sqrt(183+3*(214669+2352*sqrt(57))^(1/3)+10731/(214669+2352*sqrt(57))^(1/3))-(1/6)*sqrt(366-3*(214669+2352*sqrt(57))^(1/3)-10731/(214669+2352*sqrt(57))^(1/3)+432/sqrt(183+3*(214669+2352*sqrt(57))^(1/3)+10731/(214669+2352*sqrt(57))^(1/3)))

I got this result from Maple by solving the resolvent cubic, which did come out symbolic.  How do I get the quartic root to come out symbolic?

Thanks,

Bob Baker

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