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Austrian MO Beginners' Competition
2012 Austria Beginners' Competition
3
3
Part of
2012 Austria Beginners' Competition
Problems
(1)
4ab <= 2 (a^2+ b^2) <= 5 ab if 0< a <= 2b <= 4a
Source: Austria Beginners' Competition 2012 p3
12/26/2021
Let
a
a
a
and
b
b
b
be two positive real numbers with
a
≤
2
b
≤
4
a
a \le 2b \le 4a
a
≤
2
b
≤
4
a
. Prove that
4
a
b
≤
2
(
a
2
+
b
2
)
≤
5
a
b
4ab \le2 (a^2+ b^2) \le 5 ab
4
ab
≤
2
(
a
2
+
b
2
)
≤
5
ab
.
algebra
inequalities