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Saudi Arabia Pre-TST + Training Tests
2011 Saudi Arabia Pre-TST
1.1
8(a+b+c) (a/b+b/c +c/a) < = 9 (1+a/b) (1+b/c) (1+c/a)
8(a+b+c) (a/b+b/c +c/a) < = 9 (1+a/b) (1+b/c) (1+c/a)
Source: 2011 Saudi Arabia Pre-TST February 1.1
January 1, 2022
algebra
inequalities
Problem Statement
Let
a
,
b
,
c
a, b, c
a
,
b
,
c
be positive real numbers. Prove that
8
(
a
+
b
+
c
)
(
a
b
+
b
c
+
c
a
)
≤
9
(
1
+
a
b
)
(
1
+
b
c
)
(
1
+
c
a
)
8(a+b+c) \left(\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \right) \le 9 \left(1+\frac{a}{b} \right)\left(1+\frac{b}{c} \right)\left(1+\frac{c}{a} \right)
8
(
a
+
b
+
c
)
(
b
a
+
c
b
+
a
c
)
≤
9
(
1
+
b
a
)
(
1
+
c
b
)
(
1
+
a
c
)
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