MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia TST
2008 Indonesia TST
4
sum (a/(a+b)) ^2 >= 3/4
sum (a/(a+b)) ^2 >= 3/4
Source: 2008 Indonesia TST stage 2 test 3 p4
December 15, 2020
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive reals. Prove that
(
a
a
+
b
)
2
+
(
b
b
+
c
)
2
+
(
c
c
+
a
)
2
≥
3
4
\left(\frac{a}{a+b}\right)^2+\left(\frac{b}{b+c}\right)^2+\left(\frac{c}{c+a}\right)^2\ge \frac34
(
a
+
b
a
)
2
+
(
b
+
c
b
)
2
+
(
c
+
a
c
)
2
≥
4
3
Back to Problems
View on AoPS