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Problems
Contests
National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2004 Switzerland - Final Round
5
5
Part of
2004 Switzerland - Final Round
Problems
(1)
min sum x^2/(ay + bz)(az + by)
Source: Switzerland - 2004 Swiss MO Final Round p5
12/26/2022
Let
a
a
a
and
b
b
b
be fixed positive numbers. Find the smallest possible depending on
a
a
a
and
b
b
b
value of the sum
x
2
(
a
y
+
b
z
)
(
a
z
+
b
y
)
+
y
2
(
a
z
+
b
x
)
(
a
x
+
b
z
)
+
z
2
(
a
x
+
b
y
)
(
a
y
+
b
x
)
,
\frac{x^2}{(ay + bz)(az + by)}+\frac{y^2}{(az + bx)(ax + bz)}+\frac{z^2}{(ax + by)(ay + bx)},
(
a
y
+
b
z
)
(
a
z
+
b
y
)
x
2
+
(
a
z
+
b
x
)
(
a
x
+
b
z
)
y
2
+
(
a
x
+
b
y
)
(
a
y
+
b
x
)
z
2
,
where
x
,
y
,
z
x, y, z
x
,
y
,
z
are positive real numbers.
algebra
inequalities