MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
TST Round 2
2016 Taiwan TST Round 2
2
Inequality
Inequality
Source: 2016 Taiwan TST Round 2
July 18, 2016
inequalities
Problem Statement
Let
x
,
y
x,y
x
,
y
be positive real numbers such that
x
+
y
=
1
x+y=1
x
+
y
=
1
. Prove that
x
x
2
+
y
3
+
y
x
3
+
y
2
≤
2
(
x
x
+
y
2
+
y
x
2
+
y
)
\frac{x}{x^2+y^3}+\frac{y}{x^3+y^2}\leq2(\frac{x}{x+y^2}+\frac{y}{x^2+y})
x
2
+
y
3
x
+
x
3
+
y
2
y
≤
2
(
x
+
y
2
x
+
x
2
+
y
y
)
.
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