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3
x^2+y^2+1 >= 2(xy-x+y) Puerto Rico Ibero TST 2010.3
x^2+y^2+1 >= 2(xy-x+y) Puerto Rico Ibero TST 2010.3
Source:
September 16, 2021
algebra
inequalities
Problem Statement
Prove that the inequality
x
2
+
y
2
+
1
≥
2
(
x
y
−
x
+
y
)
x^2+y^2+1\ge 2(xy-x+y)
x
2
+
y
2
+
1
≥
2
(
x
y
−
x
+
y
)
is satisfied by any
x
x
x
,
y
y
y
real numbers. Indicate when the equality is satisfied.
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