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2014 Junior Regional Olympiad - FBH
2
Junior Regional Olympiad - FBH 2014 Grade 8 Problem 2
Junior Regional Olympiad - FBH 2014 Grade 8 Problem 2
Source:
October 3, 2018
well known
Problem Statement
Find value of
1
1
+
x
+
x
y
+
1
1
+
y
+
y
z
+
1
1
+
z
+
z
x
\frac{1}{1+x+xy}+\frac{1}{1+y+yz}+\frac{1}{1+z+zx}
1
+
x
+
x
y
1
+
1
+
y
+
yz
1
+
1
+
z
+
z
x
1
if
x
x
x
,
y
y
y
and
z
z
z
are real numbers usch that
x
y
z
=
1
xyz=1
x
yz
=
1
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