Question 69
A regular tetrahedron of height $h$ has a tetrahedron of height $xh$ cut off by a plane parallel to the base. When the remaining frustrum is placed on one of its slant faces on a horizontal plane, it is just on the point of falling over, that is the projection of the center of gravity $G$ of the frustrum is a point of the minor base of this slant face. Show that $x$ is a root of the equation:
$$
x^3 + x^2 + x = 2.
$$
$$
x^3 + x^2 + x = 2.
$$