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Nigeria Contests
Nigerian Senior Mathematics Olympiad Round 2
2016 Nigerian Senior MO Round 2
Problem 6
Simple inequality
Simple inequality
Source: 2016 Nigerian Senior MO Round 2
November 16, 2022
algebra
Inequality
inequalities
Problem Statement
Given that
a
,
b
,
c
,
d
∈
R
a, b, c, d \in \mathbb{R}
a
,
b
,
c
,
d
∈
R
, prove that
(
a
b
+
c
d
)
2
≤
(
a
2
+
c
2
)
(
b
2
+
d
2
)
(ab+cd)^2 \leq (a^2+c^2)(b^2+d^2)
(
ab
+
c
d
)
2
≤
(
a
2
+
c
2
)
(
b
2
+
d
2
)
.
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