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2014 BMT Spring
14
2014 BMT Team 14
2014 BMT Team 14
Source:
January 6, 2022
algebra
Problem Statement
Let
(
x
,
y
)
(x, y)
(
x
,
y
)
be an intersection of the equations
y
=
4
x
2
−
28
x
+
41
y = 4x^2 - 28x + 41
y
=
4
x
2
−
28
x
+
41
and
x
2
+
25
y
2
−
7
x
+
100
y
+
349
4
=
0
x^2 + 25y^2 - 7x + 100y +\frac{349}{4}= 0
x
2
+
25
y
2
−
7
x
+
100
y
+
4
349
=
0
. Find the sum of all possible values of
x
x
x
.
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