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National and Regional Contests
South Africa Contests
South Africa National Olympiad
2015 South Africa National Olympiad
2
2
Part of
2015 South Africa National Olympiad
Problems
(1)
Solutions to $5x^3 + ax^2 + 8 = 5x^3 + 8x^2 + a = 0$.
Source:
8/8/2015
Determine all pairs of real numbers
a
a
a
and
x
x
x
that satisfy the simultaneous equations
5
x
3
+
a
x
2
+
8
=
0
5x^3 + ax^2 + 8 = 0
5
x
3
+
a
x
2
+
8
=
0
and
5
x
3
+
8
x
2
+
a
=
0.
5x^3 + 8x^2 + a = 0.
5
x
3
+
8
x
2
+
a
=
0.
algebra