title: Solve finds wrong solution?
body: <p>I have this equation in x and y:</p>
  
  <pre><code>  (x + y)^(1/2) - 6*y*(x + y)^5 - (x + y)^6 + (x - 1)/(2*(x + y)^(1/2)) = 0.
  </code></pre>
  
  <p>Now I call the solver:</p>
  
  <pre><code>  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);
  </code></pre>
  
  <p>which gives me the implicit solutions as a function of y. Now try</p>
  
  <pre><code>  R_c(.3)
  </code></pre>
  
  <p>to find the explicit solution at y = 0.3. MATLAB's answer is:</p>
  
  <pre><code> ans =
  
   0.42846617518653978966562924618638
   0.15249587894102346284238111155954
   0.12068186494007759990714181154349
  </code></pre>
  
  <p>However, the last entry in this array is NOT a solution. Test:</p>
  
  <pre><code> 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))
  </code></pre>
  
  <p>yields</p>
  
  <pre><code> -0.0585.
  </code></pre>
  
  <p>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?</p>