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6
2000 KJMO if product is not smaller than the sum
2000 KJMO if product is not smaller than the sum
Source: 2000 KJMO
June 29, 2024
inequalities
algebra
Problem Statement
x
,
y
,
z
x, y, z
x
,
y
,
z
are positive reals which their product is not smaller then their sum. Prove the inequality:
2
x
2
+
y
z
+
2
y
2
+
z
x
+
2
z
2
+
x
y
≥
9
\sqrt{2x^2+yz}+\sqrt{2y^2+zx}+\sqrt{2z^2+xy} \geq 9
2
x
2
+
yz
+
2
y
2
+
z
x
+
2
z
2
+
x
y
≥
9
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