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2021 New Zealand MO
2
x^2 +8/xy + y^2 >= 8 New Zealand MO 2021 Round 2 p2 NZMO
x^2 +8/xy + y^2 >= 8 New Zealand MO 2021 Round 2 p2 NZMO
Source:
October 6, 2021
algebra
inequalities
Problem Statement
Prove that
x
2
+
8
x
y
+
y
2
≥
8
x^2 +\frac{8}{xy}+ y^2 \ge 8
x
2
+
x
y
8
+
y
2
≥
8
for all positive real numbers
x
x
x
and
y
y
y
.
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