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25
2007 Guts #25: Finding All Possible Values
2007 Guts #25: Finding All Possible Values
Source:
June 22, 2012
Problem Statement
Two real numbers
x
x
x
and
y
y
y
are such that
8
y
4
+
4
x
2
y
2
+
4
x
y
2
+
2
x
3
+
2
y
2
+
2
x
=
x
2
+
1
8y^4+4x^2y^2+4xy^2+2x^3+2y^2+2x=x^2+1
8
y
4
+
4
x
2
y
2
+
4
x
y
2
+
2
x
3
+
2
y
2
+
2
x
=
x
2
+
1
. Find all possible values of
x
+
2
y
2
x+2y^2
x
+
2
y
2
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