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2023 Assam Mathematics Olympiad
7
Assam Mathematics Olympiad 2023 Category III Q7
Assam Mathematics Olympiad 2023 Category III Q7
Source:
September 11, 2024
Problem Statement
If
x
y
z
=
1
xyz=1
x
yz
=
1
find the value of
(
1
1
+
x
+
1
y
+
1
1
+
y
+
1
z
+
1
1
+
z
+
1
x
)
2
\left(\frac{1}{1+x+\frac{1}{y}}+\frac{1}{1+y+\frac{1}{z}}+\frac{1}{1+z+\frac{1}{x}}\right)^2
(
1
+
x
+
y
1
1
+
1
+
y
+
z
1
1
+
1
+
z
+
x
1
1
)
2
.
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