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2021 MOAA
11
Team Round P11
Team Round P11
Source:
October 16, 2021
MOAA 2021
team
Problem Statement
Find the product of all possible real values for
k
k
k
such that the system of equations
x
2
+
y
2
=
80
x^2+y^2= 80
x
2
+
y
2
=
80
x
2
+
y
2
=
k
+
2
x
ā
8
y
x^2+y^2= k+2x-8y
x
2
+
y
2
=
k
+
2
x
ā
8
y
has exactly one real solution
(
x
,
y
)
(x,y)
(
x
,
y
)
.Proposed by Nathan Xiong
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