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Byju's Answer
Standard X
Mathematics
Solving a Quadratic Equation by Completion of Squares Method
For what valu...
Question
For what value of
n
,
a
2
n
+
1
+
b
2
n
+
1
a
2
n
+
b
2
n
is the arithmetic mean of a and b where
a
≠
b
.
A
1
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B
0.0
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C
-1
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D
2
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Solution
The correct option is
B
0.0
2
(
a
2
n
+
1
+
b
2
n
+
1
a
2
n
+
b
2
n
)
=
a
+
b
Solving this, we get
a
2
n
(
a
−
b
)
=
b
2
n
(
a
−
b
)
→
(
a
b
)
2
n
=
1
→
n
=
0
Suggest Corrections
0
Similar questions
Q.
For
n
∈
N
,
a
2
n
−
1
+
b
2
n
−
1
is divisible by
Q.
If
a
,
b
and
n
are natural numbers then
a
2
n
−
1
+
b
2
n
−
1
is divisible by
Q.
If
sin
4
θ
a
+
cos
4
θ
b
=
1
a
+
b
, prove that
i)
sin
8
θ
a
3
+
cos
8
θ
b
3
=
1
(
a
+
b
)
3
ii)
sin
4
n
θ
a
2
n
−
1
+
cos
4
n
θ
b
2
n
−
1
=
1
(
a
+
b
)
2
n
−
1
,
n
∈
N
Q.
If
sin
4
x
a
+
cos
4
x
b
=
1
a
+
b
, prove that
(i)
sin
8
x
a
3
+
cos
8
x
b
3
=
1
(
a
+
b
)
3
(ii)
sin
4
n
x
a
2
n
−
1
+
cos
4
n
x
b
2
n
−
1
=
1
(
a
+
b
)
2
n
−
1
,
n
∈
N
Q.
An A.P., a G.P. and H.P. have a and b for their first two terms, Show that their (n + 2) th terms will be in G.P. if
b
2
n
+
2
−
a
2
n
+
2
a
b
(
b
2
n
−
a
2
n
)
=
n
+
1
n
.
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