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The expression [x+(x^3-1)^(1/2)]^5+[x-(x...

The expression `[x+(x^3-1)^(1/2)]^5+[x-(x^3-1)^(1/2)]^5` is a polynomial of degree

A

5

B

6

C

7

D

8

Text Solution

Verified by Experts

The correct Answer is:
C
We know that,
`(a+b)^(5)+(a-b)^(5)=(.^(5)C_(0)a^5)+.^(5)C_(1)a^(4)b+.^(5)C_(2)a^(3)b^(2)`
`+.^(5)C_(3)a^(2)b^(3)+.^(5)C_(4)ab^(4)+.^(5)C_(5)b^(5)+.^(5)C_(0)a^(5)-.^(5)C_(1)a^(4)b+.^(5)C_(2)a^(3)b^(2)-.^(5)C_(3)a^(2)b^(3)+.^(5)C_(4)ab^(4)-.^(5)C_(5)b^(5)`
`=2[a^(5)+10a^(3)b^(2)+5ab^(4)]`
`therefore[x+(x^(3)-1)^(1//2)]^(5)+[x-(x^(3)-1)^(1//2)]^(5)`
`=2[x^(5)+10x^(3)(x^(3)-1)+5x(x^(3)-1)^(2)]`
Therefore, the give expression is a polynomial of degree 7.
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