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Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2005 China Second Round Olympiad
2
2
Part of
2005 China Second Round Olympiad
Problems
(1)
Minimum value of function
Source: 2005 China Second Round Olympiad
9/2/2014
Assume that positive numbers
a
,
b
,
c
,
x
,
y
,
z
a, b, c, x, y, z
a
,
b
,
c
,
x
,
y
,
z
satisfy
c
y
+
b
z
=
a
cy + bz = a
cy
+
b
z
=
a
,
a
z
+
c
x
=
b
az + cx = b
a
z
+
c
x
=
b
, and
b
x
+
a
y
=
c
bx + ay = c
b
x
+
a
y
=
c
. Find the minimum value of the function
f
(
x
,
y
,
z
)
=
x
2
x
+
1
+
y
2
y
+
1
+
z
2
z
+
1
.
f(x, y, z) = \frac{x^2}{x+1} + \frac {y^2}{y+1} + \frac{z^2}{z+1}.
f
(
x
,
y
,
z
)
=
x
+
1
x
2
+
y
+
1
y
2
+
z
+
1
z
2
.
function
inequalities unsolved
inequalities
China
algebra
inequalities proposed
Inequality