MathDB
Problems
Contests
National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2021 Moldova EGMO TST
1
1
Part of
2021 Moldova EGMO TST
Problems
(1)
\frac{a^3+a^2}{1+bc}+\frac{b^3+b^2}{1+ca}+\frac{c^3+c^2}{1+ab}\geq3.
Source: Moldova EGMO TST 2021
2/4/2023
Postive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
b
c
=
1
abc=1
ab
c
=
1
. Show that
a
3
+
a
2
1
+
b
c
+
b
3
+
b
2
1
+
c
a
+
c
3
+
c
2
1
+
a
b
≥
3.
\frac{a^3+a^2}{1+bc}+\frac{b^3+b^2}{1+ca}+\frac{c^3+c^2}{1+ab}\geq3.
1
+
b
c
a
3
+
a
2
+
1
+
c
a
b
3
+
b
2
+
1
+
ab
c
3
+
c
2
≥
3.
inequalities