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Byju's Answer
Standard XII
Mathematics
Properties of Cube Root of a Complex Number
The sum of 16...
Question
The sum of
162
th
power of the roots of the equation
x
3
−
2
x
2
+
2
x
−
1
=
0
is
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Solution
Let roots of
x
3
−
2
x
2
+
2
x
−
1
=
0
be
α
,
β
,
γ
.
(
x
3
−
1
)
−
(
2
x
2
−
2
x
)
=
0
⇒
(
x
−
1
)
(
x
2
−
x
+
1
)
=
0
⇒
x
=
1
,
−
ω
,
−
ω
2
Now,
α
162
+
β
162
+
γ
162
=
1
+
(
−
ω
)
162
+
(
−
ω
2
)
162
=
1
+
(
ω
3
)
54
+
(
ω
3
)
108
=
3
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Similar questions
Q.
The sum of
162
th
power of the roots of the equation
x
3
−
2
x
2
+
2
x
−
1
=
0
is
Q.
The sum of the fourth powers of the roots of the equation
x
3
+
x
+
1
=
0
is:
Q.
Find the sum of the fourth powers of the roots of
x
3
−
2
x
2
+
x
−
1
=
0
.
Q.
The common roots of the equations
x
3
+
2
x
2
+
2
x
+
1
=
0
and
x
+
x
2
+
x
3
=
0
are (
ω
is non real cube root of unity)
Q.
The common roots of the equation
x
3
+
2
x
2
+
2
x
+
1
=
0
and
1
+
x
130
+
x
1988
=
0
is/are
Note:
ω
is a non-real cube root of unity.
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