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National and Regional Contests
Argentina Contests
Argentina Cono Sur TST
2024 Argentina Cono Sur TST
Problem 4
Problem 4
Part of
2024 Argentina Cono Sur TST
Problems
(1)
Minimum value of fraction with three variables
Source: Argentina Cono Sur TST 2024 P4
8/9/2024
Find the least possible value of
(
x
2
+
1
)
(
4
y
2
+
1
)
(
9
z
2
+
1
)
6
x
y
z
\dfrac{(x^2+1)(4y^2+1)(9z^2+1)}{6xyz}
6
x
yz
(
x
2
+
1
)
(
4
y
2
+
1
)
(
9
z
2
+
1
)
if
x
x
x
,
y
y
y
,
z
z
z
are not necessarily distinct positive real numbers.
algebra