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2015 Korea National Olympiad
3
5-var Asymmetric Inequality
5-var Asymmetric Inequality
Source: 2015 Korean Mathematical Olympiad P3
November 1, 2015
inequalities
Problem Statement
Reals
a
,
b
,
c
,
x
,
y
a,b,c,x,y
a
,
b
,
c
,
x
,
y
satisfies
a
2
+
b
2
+
c
2
+
x
2
+
y
2
=
1
a^2+b^2+c^2+x^2+y^2=1
a
2
+
b
2
+
c
2
+
x
2
+
y
2
=
1
. Find the maximum value of
(
a
x
+
b
y
)
2
+
(
b
x
+
c
y
)
2
(ax+by)^2+(bx+cy)^2
(
a
x
+
b
y
)
2
+
(
b
x
+
cy
)
2
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