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a,b,c,d in AP and a,h,k,d in GP --> bc ≥ hk - [Canada 1979]
a,b,c,d in AP and a,h,k,d in GP --> bc ≥ hk - [Canada 1979]
Source:
September 29, 2011
arithmetic sequence
Problem Statement
Given: (i)
a
a
a
,
b
>
0
b > 0
b
>
0
; (ii)
a
a
a
,
A
1
A_1
A
1
,
A
2
A_2
A
2
,
b
b
b
is an arithmetic progression; (iii)
a
a
a
,
G
1
G_1
G
1
,
G
2
G_2
G
2
,
b
b
b
is a geometric progression. Show that
A
1
A
2
≥
G
1
G
2
.
A_1 A_2 \ge G_1 G_2.
A
1
A
2
≥
G
1
G
2
.
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