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Problem
Problem
If
α
,
β
,
γ
\alpha, \beta, \gamma
α
,
β
,
γ
are the roots of
x
3
−
x
2
+
a
x
+
b
=
0
x^3 - x^2 + ax + b = 0
x
3
−
x
2
+
a
x
+
b
=
0
and
β
,
γ
,
δ
\beta, \gamma, \delta
β
,
γ
,
δ
are the roots of
x
3
−
4
x
2
+
m
x
+
n
=
0
x^3 - 4x^2 + mx + n = 0
x
3
−
4
x
2
+
m
x
+
n
=
0
. If
α
,
β
,
γ
\alpha, \beta, \gamma
α
,
β
,
γ
and
δ
\delta
δ
are in AP with common difference
d
d
d
then a.
a
=
m
a = m
a
=
m
b.
a
=
m
−
5
a = m - 5
a
=
m
−
5
c.
n
=
b
−
a
−
2
n = b - a - 2
n
=
b
−
a
−
2
d.
b
=
m
+
n
−
3
b = m + n - 3
b
=
m
+
n
−
3
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