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National and Regional Contests
Austria Contests
Austrian MO Regional Competition
2019 Regional Competition For Advanced Students
1
Simple inequality
Simple inequality
Source: Austria 2019
June 1, 2019
inequalities
BPSQ
algebra
inequalities proposed
Problem Statement
Let
x
,
y
x,y
x
,
y
be real numbers such that
(
x
+
1
)
(
y
+
2
)
=
8.
(x+1)(y+2)=8.
(
x
+
1
)
(
y
+
2
)
=
8.
Prove that
(
x
y
−
10
)
2
≥
64.
(xy-10)^2\ge 64.
(
x
y
−
10
)
2
≥
64.
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