Russelle's triple tangent
Algebra
Level
4
Let \(x, y, z\) be the real roots of the cubic equation
\[2u^3-799u^2-400u-1=0\]
and let \(\omega = \tan^{-1} x+\tan^{-1} y+\tan^{-1} z\). If \(\tan \omega = \frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers, what is the value of \(a+b\)?
This problem is posed by Russelle G.
by
Calvin Lin