Q8.4.1Equation solving with scipy.optimize.brentq

Use scipy.optimize.brentq to find the solutions to the equation

x + 1 = -\frac{1}{(x-3)^3}

Show solution

Rewrite the equation as

f(x) = x + 1 + (x-3)^{-3} = 0.

This function is readily plotted and the roots may be bracketed in $$(-2, -0.5)$$ and $$(0, 2.99)$$ (avoiding the singularity at $$x=3$$ ).

In [x]: f = lambda x: x + 1 + (x-3)**-3
In [x]: brentq(f, -2, -0.5), brentq(f, 0, 2.99)
Out[x]: (-0.984188231211512, 2.3303684533047426)