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2023 MOAA
11
2023 MOAA Team P11
2023 MOAA Team P11
Source:
October 14, 2023
MOAA 2023
Problem Statement
Let the quadratic
P
(
x
)
=
x
2
+
5
x
+
1
P(x)=x^2+5x+1
P
(
x
)
=
x
2
+
5
x
+
1
. Two distinct real numbers
a
,
b
a,b
a
,
b
satisfy
P
(
a
+
b
)
=
a
b
P(a+b)=ab
P
(
a
+
b
)
=
ab
P
(
a
b
)
=
a
+
b
P(ab)=a+b
P
(
ab
)
=
a
+
b
Find the sum of all possible values of
a
2
a^2
a
2
.Proposed by Harry Kim
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