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Swedish Mathematical Competition
2015 Swedish Mathematical Competition
3
3
Part of
2015 Swedish Mathematical Competition
Problems
(1)
min of (a^2+2b^2+4c^2)/ b(a+2c) for a,b,c>0
Source: 2015 Swedish Mathematical Competition p3
4/30/2021
Let
a
a
a
,
b
b
b
,
c
c
c
be positive real numbers. Determine the minimum value of the following expression
a
2
+
2
b
2
+
4
c
2
b
(
a
+
2
c
)
\frac{a^2+2b^2+4c^2}{b(a+2c)}
b
(
a
+
2
c
)
a
2
+
2
b
2
+
4
c
2
algebra
min
inequalities