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2019 South East Mathematical Olympiad
6
the maximum of axy+byz+czx
the maximum of axy+byz+czx
Source: CSMO 2019 Grade 10 Problem 6
July 31, 2019
algebra
Problem Statement
Let
a
,
b
,
c
a,b,c
a
,
b
,
c
be the lengths of the sides of a given triangle.If positive reals
x
,
y
,
z
x,y,z
x
,
y
,
z
satisfy
x
+
y
+
z
=
1
,
x+y+z=1,
x
+
y
+
z
=
1
,
find the maximum of
a
x
y
+
b
y
z
+
c
z
x
.
axy+byz+czx.
a
x
y
+
b
yz
+
cz
x
.
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