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2024-IMOC
A6
A6
Part of
2024-IMOC
Problems
(1)
A strange inequality in Taiwan
Source: Own
8/2/2024
Given positive real
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfying
1
a
+
1
+
3
b
+
3
+
3
c
+
3
=
7
2
\frac{1}{\sqrt{a+1}}+\frac{3}{\sqrt{b+3}}+\frac{3}{\sqrt{c+3}}=\frac72
a
+
1
1
+
b
+
3
3
+
c
+
3
3
=
2
7
Prove that
a
b
c
≤
3
abc\leq 3
ab
c
≤
3
.\\ I was asked to propose a inequality for the condition of
a
b
c
<
3
abc<3
ab
c
<
3
inequality since <3 looks like a heart shape, then I construct a equality and with the help of wolfram, I gave the birth of this bad-looking inequality, I’m glad to see any method besides calculus.
inequalities
calculus