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National High School Mathematics League
1987 National High School Mathematics League
5
Two Equal Set
Two Equal Set
Source: 1987 National High School Mathematics League, Exam One, Problem 5
February 24, 2020
Problem Statement
Two sets
M
=
{
x
,
x
y
,
lg
(
x
y
)
}
,
N
=
{
0
,
∣
x
∣
,
y
}
M=\{x,xy,\lg(xy)\},N=\{0,|x|,y\}
M
=
{
x
,
x
y
,
l
g
(
x
y
)}
,
N
=
{
0
,
∣
x
∣
,
y
}
, if
M
=
N
M=N
M
=
N
, then
(
x
+
1
y
)
+
(
x
2
+
1
y
2
)
+
⋯
+
(
x
2001
+
1
y
2001
)
=
(x+\frac{1}{y})+(x^2+\frac{1}{y^2})+\cdots+(x^{2001}+\frac{1}{y^{2001}})=
(
x
+
y
1
)
+
(
x
2
+
y
2
1
)
+
⋯
+
(
x
2001
+
y
2001
1
)
=
________.
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