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1957 Polish MO Finals
4
\sqrt{a^2 + b^2} \geq a + b - (2 - \sqrt{2}) \sqrt{ab}
\sqrt{a^2 + b^2} \geq a + b - (2 - \sqrt{2}) \sqrt{ab}
Source: Polish MO Finals 1957 p4
August 29, 2024
algebra
inequalities
Problem Statement
Prove that if
a
≥
0
a \geq 0
a
≥
0
and
b
≥
0
b \geq 0
b
≥
0
, then
a
2
+
b
2
≥
a
+
b
−
(
2
−
2
)
a
b
.
\sqrt{a^2 + b^2} \geq a + b - (2 - \sqrt{2}) \sqrt{ab}.
a
2
+
b
2
≥
a
+
b
−
(
2
−
2
)
ab
.
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