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2023 MOAA
10
2023 MOAA Speed P10
2023 MOAA Speed P10
Source:
October 13, 2023
MOAA 2023
Problem Statement
If
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfy the system of equations
x
y
+
y
z
+
z
x
=
23
xy+yz+zx=23
x
y
+
yz
+
z
x
=
23
y
x
+
y
+
z
y
+
z
+
x
z
+
x
=
−
1
\frac{y}{x+y}+\frac{z}{y+z}+\frac{x}{z+x}=-1
x
+
y
y
+
y
+
z
z
+
z
+
x
x
=
−
1
z
2
x
x
+
y
+
x
2
y
y
+
z
+
y
2
z
z
+
x
=
202
\frac{z^2x}{x+y}+\frac{x^2y}{y+z}+\frac{y^2z}{z+x}=202
x
+
y
z
2
x
+
y
+
z
x
2
y
+
z
+
x
y
2
z
=
202
Find the value of
x
2
+
y
2
+
z
2
x^2+y^2+z^2
x
2
+
y
2
+
z
2
.Proposed by Harry Kim
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