MathDB
Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2018 Hanoi Open Mathematics Competitions
10
HOMC 2018
HOMC 2018
Source:
January 25, 2019
homc
homc2018
Problem Statement
Let
T
=
1
4
x
2
−
1
5
y
2
+
1
6
z
2
T=\frac{1}{4}x^{2}-\frac{1}{5}y^{2}+\frac{1}{6}z^{2}
T
=
4
1
x
2
−
5
1
y
2
+
6
1
z
2
where
x
,
y
,
z
x,y,z
x
,
y
,
z
are real numbers such that
1
≤
x
,
y
,
z
≤
4
1 \leq x,y,z \leq 4
1
≤
x
,
y
,
z
≤
4
and
x
−
y
+
z
=
4
x-y+z=4
x
−
y
+
z
=
4
. Find the smallest value of
10
×
T
10 \times T
10
×
T
.
Back to Problems
View on AoPS