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tetrahedron, minimize expression gives side lengths

Source: 1998 France MO P1

April 10, 2021
geometry3D geometrytetrahedroninequalities

Problem Statement

A tetrahedron ABCDABCD satisfies the following conditions: the edges AB,ACAB,AC and ADAD are pairwise orthogonal, AB=3AB=3 and CD=2CD=\sqrt2. Find the minimum possible value of BC6+BD6−AC6−AD6.BC^6+BD^6-AC^6-AD^6.
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