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Hanoi Open Mathematics Competition
2019 Hanoi Open Mathematics Competitions
9
9
Part of
2019 Hanoi Open Mathematics Competitions
Problems
(1)
min of S = 2a +3 +32/(a - b) (2b +3)^2, for a>b>0 (HOMC 2019 JI-9)
Source:
11/7/2020
Let
a
a
a
and
b
b
b
be positive real numbers with
a
>
b
a > b
a
>
b
. Find the smallest possible values of
S
=
2
a
+
3
+
32
(
a
−
b
)
(
2
b
+
3
)
2
S = 2a +3 +\frac{32}{(a - b)(2b +3)^2}
S
=
2
a
+
3
+
(
a
−
b
)
(
2
b
+
3
)
2
32
algebra
inequalities
min