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JOM 2015 Shortlist
A3
A3
Part of
JOM 2015 Shortlist
Problems
(1)
abc = 2, a, b, c <= sqrt{2}
Source: Junior Olympiad of Malaysia Shortlist 2015 A3
7/17/2015
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers less than or equal to
2
\sqrt{2}
2
such that
a
b
c
=
2
abc = 2
ab
c
=
2
, prove that
2
∑
c
y
c
a
b
+
3
c
3
a
b
+
c
≥
a
+
b
+
c
\sqrt{2}\displaystyle\sum_{cyc}\frac{ab + 3c}{3ab + c} \ge a + b + c
2
cyc
∑
3
ab
+
c
ab
+
3
c
≥
a
+
b
+
c
Inequality
inequalities