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Contests
National and Regional Contests
China Contests
China Team Selection Test
2003 China Team Selection Test
1
x+y+z=xyz
x+y+z=xyz
Source: China TST 2003
June 29, 2006
inequalities
inequalities unsolved
Problem Statement
x
x
x
,
y
y
y
and
z
z
z
are positive reals such that
x
+
y
+
z
=
x
y
z
x+y+z=xyz
x
+
y
+
z
=
x
yz
. Find the minimum value of:
x
7
(
y
z
−
1
)
+
y
7
(
z
x
−
1
)
+
z
7
(
x
y
−
1
)
x^7(yz-1)+y^7(zx-1)+z^7(xy-1)
x
7
(
yz
−
1
)
+
y
7
(
z
x
−
1
)
+
z
7
(
x
y
−
1
)
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