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2000 Moldova National Olympiad
Problem 6
max of xy, weird eq. condition
max of xy, weird eq. condition
Source: Moldova 2000 Grade 8 P6
April 25, 2021
Inequality
inequalities
Problem Statement
Assuming that real numbers
x
x
x
and
y
y
y
satisfy
y
(
1
+
x
2
)
=
x
(
1
−
4
y
2
−
1
)
y\left(1+x^2\right)=x\left(\sqrt{1-4y^2}-1\right)
y
(
1
+
x
2
)
=
x
(
1
−
4
y
2
−
1
)
, find the maximum value of
x
y
xy
x
y
.
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