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NMTC
2023 NMTC Junior
P5
NMTC 2023 Junior P5
NMTC 2023 Junior P5
Source: NMTC 2023 Junior Final P5
November 8, 2023
inequalities
nmtc
algebra
Problem Statement
a
,
b
,
c
a,b,c
a
,
b
,
c
are positive reals satisfying
2
5
≤
c
≤
min
a
,
b
\frac{2}{5} \leq c \leq \min{a,b}
5
2
≤
c
≤
min
a
,
b
;
a
c
≥
4
15
ac \geq \frac{4}{15}
a
c
≥
15
4
and
b
c
≥
1
5
bc \geq \frac{1}{5}
b
c
≥
5
1
Find the maximum value of
(
1
a
+
2
b
+
3
c
)
\left(\frac{1}{a}+\frac{2}{b}+\frac{3}{c}\right)
(
a
1
+
b
2
+
c
3
)
.
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