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2020 PUMaC Algebra A2 / B4
Source:
January 1, 2022
algebra
Problem Statement
Let
C
C
C
denote the curve
y
2
=
x
(
x
+
1
)
(
2
x
+
1
)
6
y^2 =\frac{x(x+1)(2x+1)}{6}
y
2
=
6
x
(
x
+
1
)
(
2
x
+
1
)
. The points
(
1
/
2
,
a
)
(1/2, a)
(
1/2
,
a
)
,
(
b
,
c
)
(b, c)
(
b
,
c
)
, and
(
24
,
d
)
(24, d)
(
24
,
d
)
lie on
C
C
C
and are collinear, and
a
d
<
0
ad < 0
a
d
<
0
. Given that
b
,
c
b, c
b
,
c
are rational numbers, find
100
b
2
+
c
2
100b^2 + c^2
100
b
2
+
c
2
.
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