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National and Regional Contests
Turkey Contests
Akdeniz University MO
1997 Akdeniz University MO
1
Number theory
Number theory
Source:
January 30, 2016
number theory
Discriminant
Problem Statement
Let
m
∈
R
m \in {\mathbb R}
m
∈
R
and
x
2
+
(
m
−
4
)
x
+
(
m
2
−
3
m
+
3
)
=
0
x^2+(m-4)x+(m^2-3m+3)=0
x
2
+
(
m
−
4
)
x
+
(
m
2
−
3
m
+
3
)
=
0
equations roots are
x
1
x_1
x
1
and
x
2
x_2
x
2
and
x
1
2
+
x
2
2
=
6
x_1^2+x_2^2=6
x
1
2
+
x
2
2
=
6
. Find all
m
m
m
values.
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