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03/10/13 6:55pm
In the current 9.0.1, I got
In[3]:= Solve[K == Sqrt[(M  1)/M], M]
Out[3]= {{M > 1/(1  K^2)}}
Version 5.2 solved it, too.
Since Mathematica is used a lot for creating large programs, it has to be more literal. WolframAlpha makes assumptions to make easy calculations easier.
Solve is oriented toward polynomial equations. There are some extensions.
Since Mathematica builtin names begin with capital letters, we recommend that user names begin with lowercase letters. Clashes can produce odd results.
In[1]:= ?K
K is a default generic name for a summation index in a symbolic sum.
In[2]:= ?M
Information::notfound: Symbol M not found. >>
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