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Switzerland Team Selection Test
1998 Switzerland Team Selection Test
9
frac{x}{x^4 +y^2 }+\frac{y}{x^2 +y^4} \le \frac{1}{xy}
frac{x}{x^4 +y^2 }+\frac{y}{x^2 +y^4} \le \frac{1}{xy}
Source: Switzerland - Swiss TST 1998 p9
February 19, 2020
inequalities
algebra
Problem Statement
If
x
x
x
and
y
y
y
are positive numbers, prove the inequality
x
x
4
+
y
2
+
y
x
2
+
y
4
≤
1
x
y
\frac{x}{x^4 +y^2 }+\frac{y}{x^2 +y^4} \le \frac{1}{xy}
x
4
+
y
2
x
+
x
2
+
y
4
y
≤
x
y
1
.
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