MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Akdeniz University MO
1997 Akdeniz University MO
1
1
Part of
1997 Akdeniz University MO
Problems
(2)
Number theory
Source:
1/30/2016
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.
number theory
Discriminant
equation
Source:
1/30/2016
Prove that,
15
x
2
−
7
y
2
=
9
15x^2-7y^2=9
15
x
2
−
7
y
2
=
9
equation has any solutions in integers.
equation
number theory