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### Finding root with difficulties

I'm working with this example:

sage: var('x a t', domain='real')
sage: assume(a > 0, a < 1)
sage: xt(t) = solve(integrate(-4*sqrt(17)/(9*x^2 + 6*x - 16),
...                 (x, 0, a)).subs(a = x) == t, x)[2].rhs()
sage: find_root(xt - 1, 2, 3)
0.0
sage: plot(xt - 1, (t, 2, 3))
verbose 0 (2424: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 137 points.
verbose 0 (2424: plot.py, generate_plot_points) Last error message: ''


The plot reports errors, but it looks reasonable enough. The existance of a root appears very clear, but sage is unable to find it. Furthermore, sage does not even properly report its inability to find a root, but instead returns a value as if there were no problems. The fact that this value lies outside the interval is an indication that there might be something fishy happening here.

Is there any way to get at my root numerically, or perhaps even symbolically? I know that the function xt is an ugly beast, but some form of robust bisection should be possible, I think.