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2015 Caucasus Mathematical Olympiad
2
if (x+a) (x+b) = 9 has a root a+b, prove ab <= 1
if (x+a) (x+b) = 9 has a root a+b, prove ab <= 1
Source: Caucasus 2015 11.2
April 26, 2019
algebra
inequalities
trinomial
Problem Statement
The equation
(
x
+
a
)
(
x
+
b
)
=
9
(x+a) (x+b) = 9
(
x
+
a
)
(
x
+
b
)
=
9
has a root
a
+
b
a+b
a
+
b
. Prove that
a
b
≤
1
ab\le 1
ab
≤
1
.
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