Home
Class 12
MATHS
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

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.
Promotional Banner

Similar Questions

Explore conceptually related problems

The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a polynomial of degree a. 5 b. 6 c. 7 d. 8

Expand the expression (x/3 + 1/x)^5

If a^2+b^2+c^2=-2a n df(x)= |a+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c^2)x(1+a^2)x(1+b^2)x1+c^2x| , then f(x) is a polynomial of degree 0 b. 1 c. 2 d. 3

Solve x(x+2)^2(x-1)^5(2x-3)(x-3)^4geq0.

If 2x+ [(3,1),(5,-3)]=[(-1,5),(3,-1)] then x is

Solve : (5x+2)(5x-3)(2x-1)(2x+1)=2.

The degree of polynomial 5x^(2) y+3x^(3) y^(2) +3xy+7 is …………

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)

p(x) is a polynomial of degree 1 and q(x) is a polynomial of degree 2. What kind of the polynomial p(x) xx q(x) is ?