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Chisinau City MO
1975 Chisinau City MO
104
Chisinau MO p104 1975 R2 VIII x^2+y^2>=2\sqrt2 (x-y) if xy = 1
Chisinau MO p104 1975 R2 VIII x^2+y^2>=2\sqrt2 (x-y) if xy = 1
Source:
March 16, 2021
algebra
inequalities
Problem Statement
Prove that
x
2
+
y
2
≥
2
2
(
x
−
y
)
x^2+y^2 \ge 2\sqrt2 (x-y)
x
2
+
y
2
≥
2
2
(
x
−
y
)
if
x
y
=
1
xy = 1
x
y
=
1
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