MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
Regional Olympiad - Republic of Srpska
2004 Regional Olympiad - Republic of Srpska
3
2 quadratics
2 quadratics
Source: RS2004
March 20, 2005
quadratics
algebra proposed
algebra
Problem Statement
Determine all pairs of positive integers
(
a
,
b
)
(a,b)
(
a
,
b
)
, such that the roots of the equations
x
2
−
a
x
+
a
+
b
−
3
=
0
,
x^2-ax+a+b-3=0,
x
2
−
a
x
+
a
+
b
−
3
=
0
,
x
2
−
b
x
+
a
+
b
−
3
=
0
,
x^2-bx+a+b-3=0,
x
2
−
b
x
+
a
+
b
−
3
=
0
,
are also positive integers.
Back to Problems
View on AoPS