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2023 UMD Math Competition Part I
#19
Three positive
Three positive
Source: UMD 2023 I #19
October 22, 2023
UMD
algebra
Problem Statement
Three positive real numbers
a
,
b
,
c
a, b, c
a
,
b
,
c
satisfy
a
b
=
343
,
b
c
=
10
,
a
c
=
7.
a^b = 343, b^c = 10, a^c = 7.
a
b
=
343
,
b
c
=
10
,
a
c
=
7.
Find
b
b
.
b^b.
b
b
.
a
.
1000
b
.
900
c
.
1200
d
.
4000
e
.
100
\mathrm a. ~ 1000\qquad \mathrm b.~900\qquad \mathrm c. ~1200 \qquad \mathrm d. ~4000 \qquad \mathrm e. ~100
a
.
1000
b
.
900
c
.
1200
d
.
4000
e
.
100
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