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Moldova Team Selection Test
2021 Moldova Team Selection Test
9
\frac{a^3}{1-a^2}+\frac{b^3}{1-b^2}+\frac{c^3}{1-c^2}
\frac{a^3}{1-a^2}+\frac{b^3}{1-b^2}+\frac{c^3}{1-c^2}
Source: Moldova TST 2021
September 20, 2021
inequalities
algebra
Problem Statement
Positive real numbers
a
a
a
,
b
b
b
,
c
c
c
satisfy
a
+
b
+
c
=
1
a+b+c=1
a
+
b
+
c
=
1
. Find the smallest possible value of
E
(
a
,
b
,
c
)
=
a
3
1
−
a
2
+
b
3
1
−
b
2
+
c
3
1
−
c
2
.
E(a,b,c)=\frac{a^3}{1-a^2}+\frac{b^3}{1-b^2}+\frac{c^3}{1-c^2}.
E
(
a
,
b
,
c
)
=
1
−
a
2
a
3
+
1
−
b
2
b
3
+
1
−
c
2
c
3
.
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