Given a ≥ 0 and b ≥ 0, let u = [ a b ] and v = [ b a ] . Use the Cauchy-Schwarz inequality to compare the geometric mean a b with the arithmetic mean ( a + b )/2.
Given a ≥ 0 and b ≥ 0, let u = [ a b ] and v = [ b a ] . Use the Cauchy-Schwarz inequality to compare the geometric mean a b with the arithmetic mean ( a + b )/2.
Solution Summary: The author compares the geometric mean sqrtab with the arithmetic mean, and explains the relation between the two.
Given a ≥ 0 and b ≥ 0, let
u
=
[
a
b
]
and
v
=
[
b
a
]
. Use the Cauchy-Schwarz inequality to compare the geometric mean
a
b
with the arithmetic mean (a + b)/2.
College Algebra with Modeling & Visualization (6th Edition)
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