MaplePrimes - answers and comments on Question, How do I solve this equation?

plot it

Axel Vogt — Tue, 25 Dec 2012 19:16:52 Z

plot the function and you will see where to search

gkokovidis — Tue, 25 Dec 2012 22:07:47 Z

A few more ways, to complement the plot, in order to find the real part of the solution.

Regards,

Georgios Kokovidis

Dräger Medical

toandhsp — Wed, 26 Dec 2012 06:52:24 Z

Thank you very much.

toandhsp — Wed, 26 Dec 2012 07:00:06 Z

First code

>restart:

f:=x->a/x^2-x+2:

g:=x->a*sin(2*x):

ans:=allvalues(solve(f(f(-1))=sqrt(2)+g(f(2)),a)):

ans2:=[evalf(ans)];

We get

ans2 := [-2.881759230-1.051335058*I, -.7437844448-1.866833976*I, -2.881759230+1.051335058*I, -.7437844448+1.866833976*I, -5.471111560]

Second code

>restart:

f:=x->a/x^2-x+2:

g:=x->a*sin(2*x):

ans:=fsolve(f(f(-1))=sqrt(2)+g(f(2)),a);

We get

ans := -14.51059004

The solutions -5.471111560 and -14.51059004 are different.

Carl Love — Wed, 26 Dec 2012 10:09:10 Z

Three points:

This problem is different than the one in the original post: The linear term in f has been changed from -3x to -x.
The new equation has infinitely many real solutions.
In this case, allvalues sets the global _ValuesMayBeLost to true, so the answers it gives may not include all values.