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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2006 Switzerland - Final Round
9
(a^2 + b^2 + 1)(c^2 + d^2 + 1) >= 2(a + c)(b + d)
(a^2 + b^2 + 1)(c^2 + d^2 + 1) >= 2(a + c)(b + d)
Source: Switzerland - 2006 Swiss MO Final Round p9
December 26, 2022
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be real numbers. Prove that is
(
a
2
+
b
2
+
1
)
(
c
2
+
d
2
+
1
)
≥
2
(
a
+
c
)
(
b
+
d
)
.
(a^2 + b^2 + 1)(c^2 + d^2 + 1) \ge 2(a + c)(b + d).
(
a
2
+
b
2
+
1
)
(
c
2
+
d
2
+
1
)
≥
2
(
a
+
c
)
(
b
+
d
)
.
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