MathDB
Problems
Contests
National and Regional Contests
Ireland Contests
Ireland National Math Olympiad
1993 Irish Math Olympiad
1
System of eq. of 3 degree polynomials
System of eq. of 3 degree polynomials
Source: determine sum of solution pair.
July 26, 2007
algebra
polynomial
algebra proposed
Problem Statement
The following is known about the reals
α
\alpha
α
and
β
\beta
β
α
3
−
3
α
2
+
5
α
−
17
=
0
\alpha^{3}-3\alpha^{2}+5\alpha-17=0
α
3
−
3
α
2
+
5
α
−
17
=
0
and
β
3
−
3
β
2
+
5
β
+
11
=
0
\beta^{3}-3\beta^{2}+5\beta+11=0
β
3
−
3
β
2
+
5
β
+
11
=
0
Determine
α
+
β
\alpha+\beta
α
+
β
Back to Problems
View on AoPS