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2015 Latvia Baltic Way TST
1
x^4 y^2 + y^4 + 2 x^3 y + 6 x^2 y + x^2 + 8 <= 0
x^4 y^2 + y^4 + 2 x^3 y + 6 x^2 y + x^2 + 8 <= 0
Source: 2015 Latvia BW TST P1
December 16, 2022
algebra
inequalities
Problem Statement
Given real numbers
x
x
x
and
y
y
y
, such that
x
4
y
2
+
y
4
+
2
x
3
y
+
6
x
2
y
+
x
2
+
8
≤
0.
x^4 y^2 + y^4 + 2 x^3 y + 6 x^2 y + x^2 + 8 \le 0 .
x
4
y
2
+
y
4
+
2
x
3
y
+
6
x
2
y
+
x
2
+
8
≤
0.
Prove that
x
≥
−
1
6
x \ge - \frac16
x
≥
−
6
1
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