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The sum of the co-efficients of all odd ...

The sum of the co-efficients of all odd degree terms in the expansion of `(x+sqrt(x^3-1))^5+(x-sqrt(x^3-1))^5, (x gt 1)`

A

2

B

-1

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
`(x+sqrt(x^(3)-1))^(5) + (x-sqrt(x^(3)-1))^(5)`
`= 2[.^(5)C_(0)x^(5)+.^(5)C_(2)x^(3)(sqrt(x^(3)-1))^(2) + .^(5)C_(4)x(sqrt(x^(3)-1))^(4)]`
`=2[x^(5)+10x^(3)(x^(3)-1)+5x(x^(3)-1)^(2)]`
`= 2[x^(5)+10x^(6)-10x^(3)+5x^(7)-10x^(4)+5x]`
`:.` Sum of the coeffcient of odd degree terms
`= 2(1-0+5+5) = 2`
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