A tetrahedron $ABCD$ satisfies the following conditions: the edges $AB,AC$ and $AD$ are pairwise orthogonal, $AB=3$ and $CD=\sqrt2$. Find the minimum possible value of $$BC^6+BD^6-AC^6-AD^6.$$
Source: 1998 France MO P1
Tags: geometry, 3D geometry, tetrahedron, inequalities
A tetrahedron $ABCD$ satisfies the following conditions: the edges $AB,AC$ and $AD$ are pairwise orthogonal, $AB=3$ and $CD=\sqrt2$. Find the minimum possible value of $$BC^6+BD^6-AC^6-AD^6.$$