NCERT Class XI Mathematics - Binomial Theorem - Solutions
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Question : 11
Total: 36
Find ( a + b ) 4 − ( a − b ) 4 ( √ 3 + √ 2 ) 4 − ( √ 3 − √ 2 ) 4
Solution:
By binomial theorem, we have
( a + b ) 4 − ( a − b ) 4
C 0 a 4 +
C 1 a 3 b +
C 2 a 2 b 2
C 3 a b 3 +
C 4 b 4
C 0 a 4 −
C 1 a 3 b +
C 2 a 2 b 2
C 3 a b 3 +
C 4 b 4
=a 4 + 4 a 3 b + 6 a 2 b 2 + 4 a b 3 b 4 − a 4 + 4 a 3 b − 6 a 2 b 2 4 a b 3 − b 4
∴( a + b ) 4 − ( a − b ) 4 8 a 3 b + 8 a b 3 8 a b ( a 2 + b 2 )
Substituting a =√ 3 √ 2
( √ 3 + √ 2 ) 4 − ( √ 3 − √ 2 ) 4 8 √ 3 √ 2 [ ( √ 3 ) 2 + ( √ 2 ) 2 ] 8 √ 6 [ 3 + 2 ] 40 √ 6
=
∴
Substituting a =
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