Solve finds wrong solution?

问题

I have this equation in x and y:

  (x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)) = 0.

Now I call the solver:

  R_c = @(y)solve((x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)), x, 'Real', true);

which gives me the implicit solutions as a function of y. Now try

  R_c(.3)

to find the explicit solution at y = 0.3. MATLAB's answer is:

 ans =

 0.42846617518653978966562924618638
 0.15249587894102346284238111155954
 0.12068186494007759990714181154349

However, the last entry in this array is NOT a solution. Test:

 double(subs(subs((x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)), x, .12068186494007759990714181154349), y, .3))

yields

 -0.0585.

This is not a rounding error. The other 2 solutions work perfectly and solve the equation correctly. I wonder where MATLAB the third value gets from. Can anyone help?

来源：https://stackoverflow.com/questions/24537096/solve-finds-wrong-solution