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Easy system with positive reals
Easy system with positive reals
Source: Greek IMO TST 2010 Problem 1
August 17, 2014
algebra unsolved
algebra
Problem Statement
Solve in positive reals the system:
x
+
y
+
z
+
w
=
4
x+y+z+w=4
x
+
y
+
z
+
w
=
4
1
x
+
1
y
+
1
z
+
1
w
=
5
−
1
x
y
z
w
\frac{1}{x}+\frac{1}{y}+\frac{1}{z}+\frac{1}{w}=5-\frac{1}{xyzw}
x
1
+
y
1
+
z
1
+
w
1
=
5
−
x
yz
w
1
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