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Korea Junior Mathematics Olympiad
2015 Korea Junior Math Olympiad
4
Very similar to (actually same) KMO P3
Very similar to (actually same) KMO P3
Source: 2015 Korean Junior MO P4
November 1, 2015
algebra
inequalities
Problem Statement
Reals
a
,
b
,
c
,
x
,
y
a,b,c,x,y
a
,
b
,
c
,
x
,
y
satisfy
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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