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Byju's Answer
Standard XII
Mathematics
Real Valued Functions
The expressio...
Question
The expression
x
n
−
y
n
x
2
−
y
2
is equal to
(where
x
2
≠
y
2
and
n
is even natural number greater than
6
)
A
x
n
−
1
+
x
n
−
3
y
2
+
.
.
.
+
y
n
−
2
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B
x
n
−
2
+
x
n
−
4
y
2
+
.
.
.
+
y
n
−
2
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C
x
n
−
1
+
x
n
−
2
y
2
+
.
.
.
+
y
n
−
1
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D
x
n
−
2
−
x
n
−
4
y
2
+
.
.
.
−
y
n
−
2
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Solution
The correct option is
B
x
n
−
2
+
x
n
−
4
y
2
+
.
.
.
+
y
n
−
2
Let
n
=
2
m
,
m
∈
Z
Then
x
n
−
y
n
x
2
−
y
2
=
(
x
2
)
m
−
(
y
2
)
m
x
2
−
y
2
Let
x
2
=
a
,
y
2
=
b
=
(
a
−
b
)
(
a
m
−
1
+
a
m
−
2
b
+
.
.
.
+
b
m
−
1
)
a
−
b
=
a
m
−
1
+
a
m
−
2
b
+
.
.
.
+
b
m
−
1
=
x
n
−
2
+
x
n
−
4
y
2
+
.
.
.
+
x
2
y
n
−
4
+
y
n
−
2
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1
Similar questions
Q.
lim
n
→
∞
x
n
+
y
n
x
n
−
y
n
, where
x
>
y
>
0
is equal to
Q.
Let
(
1
+
√
2
)
n
=
x
n
+
y
n
√
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where
x
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,
y
n
are integers, then
Q.
Let
¯
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be the mean of
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,
x
2
,
.
.
.
,
x
n
and
¯
y
the mean of
y
1
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y
2
,
.
.
.
,
y
n
. If
¯
z
is the mean of
x
1
,
x
2
,
.
.
.
,
x
n
,
y
1
,
y
2
,
.
.
.
,
y
n
, then
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z
is equal to
Q.
The value of
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for which
x
n
+
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+
y
n
+
1
x
n
+
y
n
is the geometric mean of
x
and
y
is
Q.
If the standard deviation of
n
observations
x
1
,
x
2
,
.
.
.
,
x
n
is
4
and another set of
n
observations
y
1
,
y
2
,
.
.
.
,
y
n
is
3
. The standard deviation of
n
observations
x
1
−
y
1
,
x
2
−
y
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,
.
.
.
,
x
n
−
y
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is
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