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Canadian Mathematical Olympiad Qualification Repechage
2017 Canadian Mathematical Olympiad Qualification
5
Inequality: (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) >= 0
Inequality: (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) >= 0
Source: Canada Repêchage 2017/5
April 13, 2017
inequalities
Problem Statement
Prove for all real numbers
x
,
y
x, y
x
,
y
,
(
x
2
+
1
)
(
y
2
+
1
)
+
4
(
x
−
1
)
(
y
−
1
)
≥
0.
(x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \geq 0.
(
x
2
+
1
)
(
y
2
+
1
)
+
4
(
x
−
1
)
(
y
−
1
)
≥
0.
Determine when equality holds.
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