the value 4√3√2^2 of is
(a)2^-1/6
(b)2^-6
(c)2^1/6
(d)2^6
Answers
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3
Answer:
Let us first expand the expression (x+1)
6
+(x−1)
6
using binomial theorem as shown below:
(x+1)
6
=
6
C
0
x
6
+
6
C
1
x
5
+
6
C
2
x
4
+
6
C
3
x
3
+
6
C
4
x
2
+
6
C
5
x
1
+
6
C
6
(x−1)
6
=
6
C
0
x
6
−
6
C
1
x
5
+
6
C
2
x
4
−
6
C
3
x
3
+
6
C
4
x
2
−
6
C
5
x
1
+
6
C
6
Now,
(x+1)
6
+(x−1)
6
=[
6
C
0
x
6
+
6
C
1
x
5
+
6
C
2
x
4
+
6
C
3
x
3
+
6
C
4
x
2
+
6
C
5
x
1
+
6
C
6
]+[
6
C
0
x
6
−
6
C
1
x
5
+
6
C
2
x
4
−
6
C
3
x
3
+
6
C
4
x
2
−
6
C
5
x
1
+
6
C
6
]
=2[
6
C
0
x
6
+
6
C
2
x
4
+
6
C
4
x
2
+
6
C
6
]
=2[x
6
+15x
4
+15x
2
+1]
By putting x=
2
, we get:
(
2
+1)
6
+(
2
−1)
6
=2[(
2
)
6
+15(
2
)
4
+15(
2
)
2
+1]
=2[8+(15×4)+(15×2)+1]
=2[8+60+30+1]
=2×99
=198
Hence, (
2
+1)
6
+(
2
−1)
6
=198.
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