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Austria Contests
Austrian MO Beginners' Competition
2008 Austria Beginners' Competition
3
3
Part of
2008 Austria Beginners' Competition
Problems
(1)
(a + b)/(a^2 -ab + b^2) <= 4/ |a + b|
Source: 2008 Austria Beginners' Competition p3
10/12/2022
Prove the inequality
a
+
b
a
2
−
a
b
+
b
2
≤
4
∣
a
+
b
∣
\frac{a + b}{a^2 -ab + b^2} \le \frac{4}{ |a + b|}
a
2
−
ab
+
b
2
a
+
b
≤
∣
a
+
b
∣
4
for all real numbers
a
a
a
and
b
b
b
with
a
+
b
≠
0
a + b\ne 0
a
+
b
=
0
. When does equality hold?
inequalities
algebra