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Problem
Problem
If
α
,
β
\alpha, \beta
α
,
β
are the roots of the equation
x
2
−
p
x
+
q
=
0
x^2 - px + q = 0
x
2
−
p
x
+
q
=
0
, find the quadratic equation the roots of which are
(
α
2
−
β
2
)
(
α
3
−
β
3
)
(\alpha^2 - \beta^2)(\alpha^3 - \beta^3)
(
α
2
−
β
2
)
(
α
3
−
β
3
)
and
α
3
β
2
+
α
2
β
3
\alpha^3\beta^2 + \alpha^2\beta^3
α
3
β
2
+
α
2
β
3
.
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