MathDB
Problems
Contests
National and Regional Contests
France Contests
French Mathematical Olympiad
1998 French Mathematical Olympiad
Problem 1
Problem 1
Part of
1998 French Mathematical Olympiad
Problems
(1)
tetrahedron, minimize expression gives side lengths
Source: 1998 France MO P1
4/10/2021
A tetrahedron
A
B
C
D
ABCD
A
BC
D
satisfies the following conditions: the edges
A
B
,
A
C
AB,AC
A
B
,
A
C
and
A
D
AD
A
D
are pairwise orthogonal,
A
B
=
3
AB=3
A
B
=
3
and
C
D
=
2
CD=\sqrt2
C
D
=
2
. Find the minimum possible value of
B
C
6
+
B
D
6
−
A
C
6
−
A
D
6
.
BC^6+BD^6-AC^6-AD^6.
B
C
6
+
B
D
6
−
A
C
6
−
A
D
6
.
geometry
3D geometry
tetrahedron
inequalities