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Regional Mathematical Olympiad
2011 India Regional Mathematical Olympiad
6
Indian RMO 2011: Question 6
Indian RMO 2011: Question 6
Source:
December 4, 2011
inequalities
Problem Statement
Find all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of real numbers such that
1
6
x
2
+
y
+
1
6
x
+
y
2
=
1
16^{x^{2}+y} + 16^{x+y^{2}} = 1
1
6
x
2
+
y
+
1
6
x
+
y
2
=
1
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