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2
sum a /\sqrt{(a + 2b)^3 \ge 1 /\sqrt{a + b + c}
sum a /\sqrt{(a + 2b)^3 \ge 1 /\sqrt{a + b + c}
Source: 2018 Romania JBMO TST 5.2
June 19, 2020
inequalities
algebra
Problem Statement
If
a
,
b
,
c
a, b, c
a
,
b
,
c
are positive real numbers, prove that
a
(
a
+
2
b
)
3
+
b
(
b
+
2
c
)
3
+
c
(
c
+
2
a
)
3
≥
1
a
+
b
+
c
\frac{a}{\sqrt{(a + 2b)^3}}+\frac{b}{\sqrt{(b + 2c)^3}} +\frac{c} {\sqrt{(c + 2a)^3}} \ge \frac{1}{\sqrt{a + b + c}}
(
a
+
2
b
)
3
a
+
(
b
+
2
c
)
3
b
+
(
c
+
2
a
)
3
c
≥
a
+
b
+
c
1
Alexandru Mihalcu
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