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2018 Turkey MO (2nd Round)
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Part of
2018 Turkey MO (2nd Round)
Problems
(1)
An equality
Source: Turkey National Mathematical Olympiad 2018
12/2/2018
Find all pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of real numbers that satisfy, \begin{align*} x^2+y^2+x+y &= xy(x+y)-\frac{10}{27}\\ |xy| & \leq \frac{25}{9}. \end{align*}
inequalities
algebra
system of equations