Solve showing more equations than I entered

I am attempting to solve a system of 3 equations. The equations contain 3 variables I am trying to solve for plus 2 parameters. I use the solve command to specify which 3 variables to solve for. However, I get a warning saying there are 6 equations in 5 variables.

Additionally, if I don't specify the variables to solve for, it still can't give me any solution.

syms a b m f r real
eq1=r*((4*b + 4*f*a)/(1 - 4*r*m)^(1/2) - 4) == 0
eq2=2*b + 2*f*a - 2*(1 - 4*r*m)^(1/2) == 0
eq3=2*f*(b+a*f-(1-4*m*r)^.5)==0
solve([eq1, eq2, eq3], [a, b, m])
Warning: 6 equations in 5 variables. 
> In C:\Program Files\MATLAB\R2013a\toolbox\symbolic\symbolic\symengine.p>symengine at 56
In mupadengine.mupadengine>mupadengine.evalin at 97
In mupadengine.mupadengine>mupadengine.feval at 150
In solve at 170 
Warning: Explicit solution could not be found. 
> In solve at 179 
solve([eq1, eq2, eq3])
Warning: Explicit solution could not be found. 
> In solve at 179

I have tried adding in some assumptions (m is negative, all other variables and parameters are positive)

assume(m<0)
assume(a>0)
assume(b>0)
assume(f>0)
assume(r>0)
solve([eq1, eq2, eq3], [a, b, m])
Warning: 6 equations in 5 variables. 
> In C:\Program Files\MATLAB\R2013a\toolbox\symbolic\symbolic\symengine.p>symengine at 56
In mupadengine.mupadengine>mupadengine.evalin at 97
In mupadengine.mupadengine>mupadengine.feval at 150
In solve at 170 
Warning: Explicit solution could not be found. 
> In solve at 179
>> solve([eq1, eq2, eq3])

ans =

    f: [1x1 sym]
    m: [1x1 sym]
    r: [1x1 sym]

 [Af, Am, Ar]=solve([eq1, eq2, eq3])

Af =

1

Am =

-1

Ar =

1

Even if I was trying to solve for f, m, and r, those solutions don't make any sense without values for b and a (to show this simply, look at equation 2 - without knowing b, there is no way to know if the left side is equal to zero.

So, I have two questions: 1) why is it telling me there are 6 equations and 5 variables? 2) Is there an exact symbolic solution and can MATLAB find it?

Answer 1

[Walter Roberson]

If you have a sufficiently old MATLAB then it might not treat the "==" as a symbolic condition to be satisfied: it might treat it as something to test immediately, discover that the symbols are not 0, and assign 0 to the variables. In such a case, remove "== 0" tests and replace "a == b" tests with (a)-(b)

I do not have the symbolic toolbox to test with, but the solution is b = -f*a+sqrt(-4*m*r+1) for all a and m