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1964 German National Olympiad
1
1
Part of
1964 German National Olympiad
Problems
(1)
\frac{a + b}{2} \ge \sqrt[a+b]{a^b b^a}
Source: 1963-64 Germany R4 12.1
10/12/2024
Prove that for all positive, entirely rational numbers
a
a
a
and
b
b
b
always holds
a
+
b
2
≥
a
b
⋅
b
a
a
+
b
.
\frac{a + b}{2} \ge \sqrt[a+b]{a^b \cdot b^a}.
2
a
+
b
≥
a
+
b
a
b
⋅
b
a
.
When does the equal sign hold?
algebra
inequalities