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Argentina National Olympiad
2021 Argentina National Olympiad
4
Argentina MO 2021 National Level 3 P4
Argentina MO 2021 National Level 3 P4
Source:
April 24, 2022
algebra
Argentina
contests
Problem Statement
Find the real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
such that,
1
x
+
1
y
+
z
=
1
2
,
1
y
+
1
z
+
x
=
1
3
,
1
z
+
1
x
+
y
=
1
4
.
\frac{1}{x}+\frac{1}{y+z}=\frac{1}{2}, \frac{1}{y}+\frac{1}{z+x}=\frac{1}{3}, \frac{1}{z}+\frac{1}{x+y}=\frac{1}{4}.
x
1
+
y
+
z
1
=
2
1
,
y
1
+
z
+
x
1
=
3
1
,
z
1
+
x
+
y
1
=
4
1
.
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