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2009 Greece Team Selection Test
3
Find all triples of reals...
Find all triples of reals...
Source: 2009 Greek TST,Pr.3
May 24, 2016
algebra
Problem Statement
Find all triples
(
x
,
y
,
z
)
∈
R
3
(x,y,z)\in \mathbb{R}^{3}
(
x
,
y
,
z
)
∈
R
3
such that
x
,
y
,
z
>
3
x,y,z>3
x
,
y
,
z
>
3
and
(
x
+
2
)
2
y
+
z
−
2
+
(
y
+
4
)
2
z
+
x
−
4
+
(
z
+
6
)
2
x
+
y
−
6
=
36
\frac{(x+2)^2}{y+z-2}+\frac{(y+4)^2}{z+x-4}+\frac{(z+6)^2}{x+y-6}=36
y
+
z
−
2
(
x
+
2
)
2
+
z
+
x
−
4
(
y
+
4
)
2
+
x
+
y
−
6
(
z
+
6
)
2
=
36
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