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A7
$\frac{a^3 + bc}{a^2 + bc}$
$\frac{a^3 + bc}{a^2 + bc}$
Source: Junior Olympiad of Malaysia Shortlist 2015 A7
July 17, 2015
Inequality
inequalities
Problem Statement
Given positive reals
a
,
b
,
c
a, b, c
a
,
b
,
c
that satisfy
a
+
b
+
c
=
1
a + b + c = 1
a
+
b
+
c
=
1
, show that
∑
c
y
c
a
3
+
b
c
a
2
+
b
c
≥
2
\displaystyle \sum^{}_{cyc}\frac{a^3+bc}{a^2+bc}\ge 2
cyc
∑
a
2
+
b
c
a
3
+
b
c
≥
2
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