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Mathematics
Problem
The solutions of the equation
x
2
+
p
x
+
q
=
0
x^2 + px + q = 0
x
2
+
p
x
+
q
=
0
are the cubes of the solutions of the equation
x
2
+
m
x
+
n
=
0
x^2 + mx + n = 0
x
2
+
m
x
+
n
=
0
. Prove that
p
=
m
3
−
3
m
n
p = m^3 - 3mn
p
=
m
3
−
3
mn
.
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