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Vietnam National Olympiad
1998 Vietnam National Olympiad
2
find min
find min
Source: 36-th Vietnamese Mathematical Olympiad 1998
February 17, 2007
analytic geometry
trigonometry
inequalities proposed
inequalities
Problem Statement
Find minimum value of
F
(
x
,
y
)
=
(
x
+
1
)
2
+
(
y
−
1
)
2
+
(
x
−
1
)
2
+
(
y
+
1
)
2
+
(
x
+
2
)
2
+
(
y
+
2
)
2
F(x,y)=\sqrt{(x+1)^{2}+(y-1)^{2}}+\sqrt{(x-1)^{2}+(y+1)^{2}}+\sqrt{(x+2)^{2}+(y+2)^{2}}
F
(
x
,
y
)
=
(
x
+
1
)
2
+
(
y
−
1
)
2
+
(
x
−
1
)
2
+
(
y
+
1
)
2
+
(
x
+
2
)
2
+
(
y
+
2
)
2
, where
x
,
y
∈
R
x,y\in\mathbb{R}
x
,
y
∈
R
.
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