MaplePrimes - answers and comments on Question, how to solve this fourth degree equation

well ...

Axel Vogt — Wed, 09 Mar 2011 02:08:33 Z

1. enter as text, so one can copy

2. a = 0 or not ?

3. ?allvalues

explicit

Robert Israel — Wed, 09 Mar 2011 02:15:55 Z

If you really want the solution in radicals of a quartic, you can use

> solve(yourequation, a, explicit);

or in older versions of Maple

> _EnvExplicit:= true;
solve(yourequation, a);

Caution: the results are not going to be pretty. For most purposes, the RootOf's are easier to deal with. What do you want to do with the solution?

thank you and you are right

barefoot1980 — Wed, 09 Mar 2011 02:52:21 Z

thank you and you are right it ain't looking pretty.

any idea to make it look nice (manageable) by some approximation

approximation

Robert Israel — Wed, 09 Mar 2011 21:51:48 Z

@barefoot1980 : An approximation might correspond to a limit where some of the parameters go to specified values, hopefully where an exact solution is known for those specified values. For example, in your equation you could take x -> infinity, and one solution is approximately

> asympt(RootOf(-x^8*a^4 + 48*z^4 + 48*x^7*a + 8*z*x^6*a-1, a), x, 10);