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2010 Saudi Arabia Pre-TST
4.3
sum (a-2)/(a+1) >= 0 if abc = 8, a,b,c>0 2010 Saudi Arabia Pre-TST 4.3
sum (a-2)/(a+1) >= 0 if abc = 8, a,b,c>0 2010 Saudi Arabia Pre-TST 4.3
Source:
December 28, 2021
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers such that
a
b
c
=
8
abc = 8
ab
c
=
8
. Prove that
a
−
2
a
+
1
+
b
−
2
b
+
1
+
c
−
2
c
+
1
≤
0
\frac{a-2}{a+1}+\frac{b-2}{b+1}+\frac{c-2}{c+1} \le 0
a
+
1
a
−
2
+
b
+
1
b
−
2
+
c
+
1
c
−
2
≤
0
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