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National and Regional Contests
Greece Contests
Greece JBMO TST
2010 Greece JBMO TST
2
(x-2y)/y + (2y-4)/x + 4/xy = 0 and 1/x + 1/y+ 1/z =2
(x-2y)/y + (2y-4)/x + 4/xy = 0 and 1/x + 1/y+ 1/z =2
Source: Greece JBMO TST 2010 p2
April 29, 2019
algebra
system of equations
Problem Statement
Find all real
x
,
y
,
z
x,y,z
x
,
y
,
z
such that
x
−
2
y
y
+
2
y
−
4
x
+
4
x
y
=
0
\frac{x-2y}{y}+\frac{2y-4}{x}+\frac{4}{xy}=0
y
x
−
2
y
+
x
2
y
−
4
+
x
y
4
=
0
and
1
x
+
1
y
+
1
z
=
2
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=2
x
1
+
y
1
+
z
1
=
2
.
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