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Problem 1
sum(x/(y^2+z))>=9/4 if x+y+z=1
sum(x/(y^2+z))>=9/4 if x+y+z=1
Source: Serbia MO 2006 3&4th Grades P1
April 10, 2021
Inequality
inequalities
algebra
Problem Statement
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be positive numbers with the sum
1
1
1
. Prove that
x
y
2
+
z
+
y
z
2
+
x
+
z
x
2
+
y
≥
9
4
.
\frac x{y^2+z}+\frac y{z^2+x}+\frac z{x^2+y}\ge\frac94.
y
2
+
z
x
+
z
2
+
x
y
+
x
2
+
y
z
≥
4
9
.
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