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2014 Cuba MO
8
8
Part of
2014 Cuba MO
Problems
(1)
3ab < 1 if ax^2 +b=x+1/x has ezctly 2 roots
Source: 2014 Cuba 2.8
9/20/2024
Let
a
a
a
and
b
b
b
be real numbers. It is known that the graph of the parabola
y
=
a
x
2
+
b
y =ax^2 +b
y
=
a
x
2
+
b
cuts the graph of the curve
y
=
x
+
1
/
x
y = x+1/x
y
=
x
+
1/
x
in exactly three points. Prove that
3
a
b
<
1
3ab < 1
3
ab
<
1
.
algebra
inequalities