Let $a$ be a non-negative real number, $b_1, b_2, b_3$ be real numbers, and $x, y, z$ be variables. Is it possible to analytically find the root closest to origin $(0, 0, 0)$ of the set of nonlinear equations given by:
$$\begin{cases} ax + yz = b_1\\ ay + xz = b_2\\ az + xy = b_3\;\;\; ?\end{cases}$$
Edit: This question is related to my research on quadrotor control. The roots of the set of nonlinear equations give the equilibrium points of the rigid body dynamics under a specific control input. I couldn't find any solution. I can only solve the problem when at least two of the $ b_1 $, $ b_2 $, and $ b_3 $ are zero.