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Problem 2
inequality, sum of a^2/(a+b)(a+c) (Croatian MO 2004 2nd Grade P2)
inequality, sum of a^2/(a+b)(a+c) (Croatian MO 2004 2nd Grade P2)
Source:
April 8, 2021
inequalities
Problem Statement
If
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive numbers, prove the inequality
a
2
(
a
+
b
)
(
a
+
c
)
+
b
2
(
b
+
c
)
(
b
+
a
)
+
c
2
(
c
+
a
)
(
c
+
b
)
≥
3
4
.
\frac{a^2}{(a+b)(a+c)}+\frac{b^2}{(b+c)(b+a)}+\frac{c^2}{(c+a)(c+b)}\ge\frac34.
(
a
+
b
)
(
a
+
c
)
a
2
+
(
b
+
c
)
(
b
+
a
)
b
2
+
(
c
+
a
)
(
c
+
b
)
c
2
≥
4
3
.
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