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Junior Tuymaada Olympiad
2003 Junior Tuymaada Olympiad
5
x^2 \sqrt {1+2y^2} + y^2 \sqrt {1+2x^2} \geq xy (x+y+\sqrt{2})
x^2 \sqrt {1+2y^2} + y^2 \sqrt {1+2x^2} \geq xy (x+y+\sqrt{2})
Source: Tuymaada Junior 2003 p5
May 11, 2019
algebra
radical inequality
Inequality
Problem Statement
Prove that for any real
x
x
x
and
y
y
y
the inequality
x
2
1
+
2
y
2
+
y
2
1
+
2
x
2
≥
x
y
(
x
+
y
+
2
)
x^2 \sqrt {1+2y^2} + y^2 \sqrt {1+2x^2} \geq xy (x+y+\sqrt{2})
x
2
1
+
2
y
2
+
y
2
1
+
2
x
2
≥
x
y
(
x
+
y
+
2
)
.
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