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2021 MOAA
7
Speed P7
Speed P7
Source:
October 16, 2021
MOAA 2021
speed
Problem Statement
If positive real numbers
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfy the following system of equations, compute
x
+
y
+
z
x+y+z
x
+
y
+
z
.
x
y
+
y
z
=
30
xy+yz = 30
x
y
+
yz
=
30
y
z
+
z
x
=
36
yz+zx = 36
yz
+
z
x
=
36
z
x
+
x
y
=
42
zx+xy = 42
z
x
+
x
y
=
42
Proposed by Nathan Xiong
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