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Byju's Answer
Standard XII
Mathematics
Constant Function
A real value ...
Question
A real value of
x
will satisfy the equation
3
−
4
i
x
3
+
4
i
x
=
α
−
i
β
(
α
,
β
∈
R
)
, if
A
α
2
−
β
2
=
−
1
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B
α
2
−
β
2
=
1
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C
α
2
+
β
2
=
1
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D
α
2
−
β
2
=
2
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Solution
The correct option is
C
α
2
+
β
2
=
1
Given
3
−
4
i
x
3
+
4
i
x
=
α
−
i
β
(
α
,
β
∈
R
)
⟹
(
3
−
4
i
x
)
2
(
3
+
4
i
x
)
(
3
−
4
i
x
)
=
α
−
i
β
(
α
,
β
∈
R
)
⟹
9
−
16
x
2
−
24
x
i
9
+
16
x
2
=
α
−
i
β
(
α
,
β
∈
R
)
comparing we get
α
=
(
9
−
16
x
2
)
(
9
+
16
x
2
)
and
β
=
(
24
)
(
9
+
16
x
2
)
Also,
α
2
+
β
2
=
(
9
−
16
x
2
)
2
+
24
2
(
9
+
16
x
2
)
2
(
9
+
16
x
2
)
2
=
1
Hence
x
satisfies the above equation.
Suggest Corrections
0
Similar questions
Q.
If variable parameter
α
,
β
,
γ
∈
R
and satisfy the relations
α
2
+
2
β
2
+
3
α
=
1
+
γ
2
and
2
α
2
+
4
β
2
=
2
γ
2
+
5
β
,
then
Q.
If
α
,
β
are real and
α
2
,
−
β
2
are the roots of the equations
a
2
x
2
+
x
+
(
1
−
a
2
)
=
0
,
a
>
1
, then
β
2
=
Q.
lf
α
,
β
are real and
α
2
,
−
β
2
are the roots of the equation
a
2
x
2
+
x
+
(
1
−
a
2
)
=
0
(
a
>
1
)
, then
β
2
=
Q.
If
α
,
β
are the roots of the equation
x
2
−
p
(
x
+
1
)
−
c
=
0
, then the value of
α
2
+
2
α
+
1
α
2
+
2
α
+
c
+
β
2
+
2
β
+
1
β
2
+
2
β
+
c
is
Q.
Let
α
,
β
are roots of the equation
x
2
−
p
(
x
+
1
)
−
q
=
0
,
then the value of
α
2
+
2
α
+
1
α
2
+
2
α
+
q
+
β
2
+
2
β
+
1
β
2
+
2
β
+
q
is
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