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Putnam
1977 Putnam
A1
A1
Part of
1977 Putnam
Problems
(1)
Putnam 1977 A1
Source:
4/7/2022
Consider all lines which meet the graph of
y
=
2
x
4
+
7
x
3
+
3
x
−
5
y=2x^4+7x^3+3x-5
y
=
2
x
4
+
7
x
3
+
3
x
−
5
in four distinct points, say
(
x
i
,
y
i
)
,
i
=
1
,
2
,
3
,
4.
(x_i,y_i), i=1,2,3,4.
(
x
i
,
y
i
)
,
i
=
1
,
2
,
3
,
4.
Show that
x
1
+
x
2
+
x
3
+
x
4
4
\frac{x_1+x_2+x_3+x_4}{4}
4
x
1
+
x
2
+
x
3
+
x
4
is independent of the line and find its value.
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