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Mathematics
Mathematics
Problem
Let
a
a
a
,
b
b
b
and
c
c
c
be three distinct real roots of the cubic
x
3
+
2
x
2
−
4
x
−
4
=
0
x^3 + 2x^2 - 4x - 4 = 0
x
3
+
2
x
2
−
4
x
−
4
=
0
. If the equation
x
3
+
q
x
2
+
r
x
+
s
=
0
x^3 + qx^2 + rx + s = 0
x
3
+
q
x
2
+
r
x
+
s
=
0
has roots
1
a
\frac{1}{a}
a
1
,
1
b
\frac{1}{b}
b
1
and
1
c
\frac{1}{c}
c
1
, then the value of
(
q
+
r
+
s
)
(q + r + s)
(
q
+
r
+
s
)
is equal to
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