The region of allowed values for solving the equation in Mathematica

Question

In[2]:= Solve[sqrt(2x-9) == sqrt(4x+3), x]

Out[2]= {{x -> -6}}

But mathematically there is no solution, since sqrt (-21) is not defined. There is a flag that is responsible for this?

You can consider asking future Mathematica-related questions on Mathematica.SE — Szabolcs, Apr 20 '12 at 16:09

Szabolcs · Accepted Answer · 2012-04-20 16:09:03Z

5

By default, Mathematica assumes that all variables are complex numbers, and when working in the set of complex numbers, Sqrt[-21] is well defined.

You can tell Mathematica (version 8) that you are working on the set of reals using

Solve[Sqrt[2 x - 9] == Sqrt[4 x + 3], x, Reals]

which gives no solution. For versions earlier than 8, you need to use Reduce if you want to specify a domain.

answered Apr 20 '12 at 16:09

Szabolcs

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Aron Ahmadia · Accepted Answer · 2012-04-20 15:55:34Z

2

Try using the Reduce equation while requiring x to belong to the Reals. See the Mathematica documentation for an example.

answered Apr 20 '12 at 15:55

Aron Ahmadia

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$\begingroup$ pastebin.com/es8Zq756 Almost the same thing. $\endgroup$
– Ticksy
Apr 20 '12 at 16:01
$\begingroup$ @Ticksy You are using incorrect syntax. Please look at some examples in the docs. It's Sqrt[x], not sqrt(x). $\endgroup$
– Szabolcs
Apr 20 '12 at 16:15

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2 Answers 2