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Junior Balkan MO
2007 Junior Balkan MO
1
1
Part of
2007 Junior Balkan MO
Problems
(1)
equation with no real solution
Source: JBMO 2007, Bulgaria, problem 1
6/28/2007
Let
a
a
a
be positive real number such that
a
3
=
6
(
a
+
1
)
a^{3}=6(a+1)
a
3
=
6
(
a
+
1
)
. Prove that the equation
x
2
+
a
x
+
a
2
ā
6
=
0
x^{2}+ax+a^{2}-6=0
x
2
+
a
x
+
a
2
ā
6
=
0
has no real solution.
quadratics
inequalities
function
algebra
algebra solved
inequalities solved
JBMO