# Calculus Allowed (But It Won't Be Pretty)

Geometry Level 4

If the maximum value of $\sqrt{x^{4} -3x^{2}+ 6x+ 13} - \sqrt{x^{4} -x^{2}+ 1}$ is of the form $$\sqrt{\alpha}$$ for all real $$x$$, then find $$\alpha$$.

×