MathDB
Problems
Contests
National and Regional Contests
Bangladesh Contests
Bangladesh Mathematical Olympiad
2019 Bangladesh Mathematical Olympiad
2
BdMO National Higher Secondary 2019/2
BdMO National Higher Secondary 2019/2
Source: BdMO National Higher Secondary 2019/2
March 4, 2019
algebra
Problem Statement
Prove that,if
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive real numbers,
a
b
c
+
b
c
a
+
c
a
b
≥
2
a
+
2
b
−
2
c
\dfrac{a}{bc}+ \dfrac{b}{ca}+\dfrac{c}{ab}\geq \dfrac{2}{a}+\dfrac{2}{b}-\dfrac{2}{c}
b
c
a
+
c
a
b
+
ab
c
≥
a
2
+
b
2
−
c
2
Back to Problems
View on AoPS