title: How to solve this system of two equations in SymPy?
body: <p>I have the function:</p>
  
  <pre><code>f(x) = 1 / (x + a)^t + b
  </code></pre>
  
  <p>And I would like to solve for a given <code>t</code> for <code>a</code> and <code>b</code> the equation system <code>{f(0)=1 and f(1)=0}</code>.</p>
  
  <p>For t=1 a solution is successfully calculated:</p>
  
  <pre><code>import sympy as sp
  a,b = sp.symbols("a b")
  res = sp.solve([1/(a+1)**1 +b, 1/a**1+b-1], [a,b])
  res
  # [(-1/2 + sqrt(5)/2, -sqrt(5)/2 + 1/2), (-sqrt(5)/2 - 1/2, 1/2 + sqrt(5)/2)]
  </code></pre>
  
  <p>But for any t other than 1 (and most of the time also 2) no solution is found:</p>
  
  <pre><code>import sympy as sp
  a,b = sp.symbols("a b")
  res = sp.solve([1/(a+1)**1.5 +b, 1/a**1.5+b-1], [a,b])
  res
  </code></pre>
  
  <p>gives:</p>
  
  <pre><code>NotImplementedError: could not solve 
  b*(-(1 + sqrt(3)*I)*(1/(b**2 - 2*b + 1))**(1/3)/2 + 1)**(3/2) + 1
  </code></pre>
  
  <hr>
  
  <p>Is it possible to approach this problem in SymPy from a more efficient angle?</p>
  
  <p>Suggestions for Python packages useful for tackling this are also most welcome.</p>