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A2
x+y<0 if x^2/y^2+y^2/x^2+x/y+y/x=0 OLCOMA Costa Rica 2015 SL A2 day2
x+y<0 if x^2/y^2+y^2/x^2+x/y+y/x=0 OLCOMA Costa Rica 2015 SL A2 day2
Source:
September 30, 2021
inequalities
algebra
Problem Statement
Determine, if they exist, the real values of
x
x
x
and
y
y
y
that satisfy that
x
2
y
2
+
y
2
x
2
+
x
y
+
y
x
=
0
\frac{x^2}{y^2} +\frac{y^2}{x^2} +\frac{x}{y}+\frac{y}{x} = 0
y
2
x
2
+
x
2
y
2
+
y
x
+
x
y
=
0
such that
x
+
y
<
0.
x + y <0.
x
+
y
<
0.
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