NCERT Class XI Mathematics - Binomial Theorem - Solutions
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Question : 12
Total: 36
Find ( x + 1 ) 6 + ( x − 1 ) 6 ( √ 2 + 1 ) 6 + ( √ 2 − 1 ) 6
Solution:
By using binomial theorem, we have
( x + 1 ) 6 + ( x − 1 ) 6
C 0 x 6 +
C 1 x 5 +
C 2 x 4
C 3 x 3 +
C 4 x 2 +
C 5 x +
C 6
C 0 + x 6 −
C 1 x 5 +
C 2 x 4
C 3 x 3 +
C 4 x 2 −
C 5 x +
C 6
=x 6 + 6 x 5 + 15 x 4 + 20 x 3 + 15 x 2 x 6 − 6 x 5 + 15 x 4 − 20 x 3 + 15 x 2
∴( x + 1 ) 6 + ( x − 1 ) 6 2 x 6 + 30 x 4 + 30 x 2
Substituting x =√ 2
( √ 2 + 1 ) 6 + ( √ 2 − 1 ) 6 2 ( √ 2 ) 6 + 30 ( √ 2 ) 4 + 30 ( √ 2 ) 2 + 2
= 16 + 120 + 60 + 2 = 198
=
∴
Substituting x =
= 16 + 120 + 60 + 2 = 198
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