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Byju's Answer
Standard XII
Mathematics
Algebra of Complex Numbers
Prove that ...
Question
Prove that
√
1
0
{
(
√
1
0
+
1
)
100
−
(
√
1
0
−
1
)
100
}
is a whole number.
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Solution
We have
{
(
√
1
0
+
1
)
100
−
(
√
1
0
−
1
)
100
}
=
2
{
100
C
1
.
(
√
10
)
+
100
C
3
.
(
√
10
)
3
+
.
.
.
.
.
.
+
100
C
99
.
(
√
10
)
99
}
=
2
√
10
{
100
C
1
.
+
100
C
3
.
(
√
10
)
2
+
.
.
.
.
.
.
+
100
C
99
.
(
√
10
)
98
}
.......(1).
∴
√
10
{
(
√
1
0
+
1
)
100
−
(
√
1
0
−
1
)
100
}
=
20
{
100
C
1
.
+
100
C
3
.
(
√
10
)
2
+
.
.
.
.
.
.
+
100
C
99
.
(
√
10
)
98
}
[Using (1)].
Each term inside and outside of the brackets are whole and hence their addition and multiplication is going to be a whole number.
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Similar questions
Q.
√
10
{
(
√
10
+
1
)
100
−
(
√
10
−
1
)
100
}
is whole number.
Q.
If
A
=
1
0
-
2
3
-
1
0
-
2
1
1
,
B
=
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-
4
-
2
1
3
-
1
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2
and
C
=
1
5
2
-
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1
0
0
-
1
1
, verify that A (B − C) = AB − AC.
Q.
In the following series, find the next term.
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,
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,
1100
,
11000
,
121000
,
1210000
Q.
By giving a discount of
10
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on the marked price of Rs.
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Q.
Let a
n
be the nth term of the G.P. of positive numbers. Let
∑
n
=
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2
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