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Contests
National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2002 Swedish Mathematical Competition
5
5
Part of
2002 Swedish Mathematical Competition
Problems
(1)
a+b =? if a^3 - 3a^2 + 5a - 17 = 0 and b^3 - 3b^2 + 5b + 11 = 0
Source: 2002 Swedish Mathematical Competition p5
3/21/2021
The reals
a
,
b
a, b
a
,
b
satisfy
{
a
3
−
3
a
2
+
5
a
−
17
=
0
b
3
−
3
b
2
+
5
b
+
11
=
0.
\begin{cases} a^3 - 3a^2 + 5a - 17 = 0 \\ b^3 - 3b^2 + 5b + 11 = 0 .\end{cases}
{
a
3
−
3
a
2
+
5
a
−
17
=
0
b
3
−
3
b
2
+
5
b
+
11
=
0.
Find
a
+
b
a+b
a
+
b
.
system of equations
System
algebra