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No solution with "Solve"

Posted 3 years ago

Hey guys, have a look at the following:

In[1]:= Solve[x^2 + 4 > 5*Abs[x], x]

During evaluation of In[1]:= Solve::fulldim: The solution set contains a full-dimensional component; use Reduce for complete solution information.

Out[1]= {{}}

As you can see, Wolfram Mathematica is not able to provide a correct solution. But the equation should definitely have a solution, I tried it with Maple.

Can you guys help me out with this problem?

Greetings.

POSTED BY: Christoph W
6 Replies
Posted 3 years ago

Ah, understood.

Thank you.

Greetings.

POSTED BY: Christoph W
Posted 3 years ago

Hey, to be honest I do not know how to use "Reduce" now. Should I apply it like that?

In[14]:= Reduce[Solve[x^2 + 4 > 5*Abs[x], x]]

During evaluation of In[14]:= Solve::fulldim: The solution set contains a full-dimensional component; use Reduce for complete solution information.

During evaluation of In[14]:= Reduce::naqs: {} is not a quantified system of equations and inequalities.

Out[14]= Reduce[{{}}]

That does not help.

Can you help me out?

Greetings.

POSTED BY: Christoph W

Check Help > Wolfram Documentation > Reduce for details on how to use that function.

POSTED BY: Daniel Lichtblau
Posted 3 years ago

Hey, thank you for answering:

In[15]:= Reduce[x^2 + 4 > 5*Abs[x], x]

Out[15]= x < -4 || -1 < x < 1 || x > 4

This actually works. Nice. Can you tell me why?

The solution set contains a full-dimensional component I don't really know what that should mean.

Greetings.

POSTED BY: Christoph W

Solve gives you a set of solutions of the form of replacement rules {{x->s1}, {s->s2},...} where s1 et al. are the solutions. Reduce gives you a reduced form for the input expression.

How would you expect Solve to express this solution set as replacement rules? I suppose it could yield a discontinuous Piecewise function of a real parameter, but I think that's obscure and unlikely to be useful. So, it gives you an error, obscure as to the cause, but clear and concrete about the fix. While the solution set isn't reasonably represented by replacement rules, reducing an expression to an equivalent expression is possible here, and seems a useful way to represent the solution set.

POSTED BY: John Doty

Did you try what is suggested in the warning message? It seems like fairly clear wording.

POSTED BY: Daniel Lichtblau
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