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Hanoi Open Mathematics Competition
2010 Hanoi Open Mathematics Competitions
10
10
Part of
2010 Hanoi Open Mathematics Competitions
Problems
(1)
max of x/(2x + y) +y/(2y + z)+z/(2z + x) in R^+ (HOMC 2010 J Q10)
Source:
7/25/2019
Find the maximum value of
M
=
x
2
x
+
y
+
y
2
y
+
z
+
z
2
z
+
x
M =\frac{x}{2x + y} +\frac{y}{2y + z}+\frac{z}{2z + x}
M
=
2
x
+
y
x
+
2
y
+
z
y
+
2
z
+
x
z
,
x
,
y
,
z
>
0
x,y, z > 0
x
,
y
,
z
>
0
algebra
maximum
inequalities