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Source:
September 9, 2023
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
be real numbers for which
a
2
+
b
2
+
c
2
+
d
2
=
1
a^2 + b^2 + c^2 + d^2 = 1
a
2
+
b
2
+
c
2
+
d
2
=
1
. Show the following inequality:
a
2
+
b
2
−
c
2
−
d
2
≤
2
+
4
(
a
c
+
b
d
)
.
a^2 + b^2 - c^2 - d^2 \le \sqrt{2 + 4(ac + bd)}.
a
2
+
b
2
−
c
2
−
d
2
≤
2
+
4
(
a
c
+
b
d
)
.
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