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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

-1

B

0

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
`= (a + b)^(n) + (a - b)^(n)`
`= 2 (.^(n)C_(0) a^(n) + .^(n)C_(2) a^(n - 2) b^(2) + .^(n)C_(4) a^(n - 4) b^(4) + …)`
We have , `(x + sqrt(x^(3) - 1))^(5) + (x - sqrt(x^(3) - 1))^(5), x gt 1`
`= 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) + 10 x^(3) (x^(3) - 1) + 5x(x^(3) - 1)^(2))`
`= 2 (x^(5) + 10x^(6) - 10 x^(3) + 5x^(7) - 10x^(4) + 5x)`
Sum of coefficients of all degree terms is
`2 (1 - 10 + 5 + 5) = 2`
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