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1
2016 Algebra Tiebreaker #1
2016 Algebra Tiebreaker #1
Source:
August 8, 2022
2016
Algebra Tiebreaker
Problem Statement
Let
x
x
x
and
y
y
y
be positive real numbers such that
x
+
y
=
1
x
+
1
y
=
5
x+y=\tfrac{1}{x}+\tfrac{1}{y}=5
x
+
y
=
x
1
+
y
1
=
5
. Compute
x
2
+
y
2
x^2+y^2
x
2
+
y
2
.
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