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National High School Mathematics League
1997 National High School Mathematics League
7
Two Numbers
Two Numbers
Source: 1997 National High School Mathematics League, Exam One, Problem 7
March 4, 2020
Problem Statement
Real numbers
x
,
y
x,y
x
,
y
satisfy that
{
(
x
−
1
)
3
+
1997
(
x
−
1
)
=
−
1
(
y
−
1
)
3
+
1997
(
y
−
1
)
=
1
\begin{cases} (x-1)^3+1997(x-1)=-1\\ (y-1)^3+1997(y-1)=1 \end{cases}
{
(
x
−
1
)
3
+
1997
(
x
−
1
)
=
−
1
(
y
−
1
)
3
+
1997
(
y
−
1
)
=
1
, then
x
+
y
=
x+y=
x
+
y
=
________.
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