Solveeit Logo
Login

Question

Question: The expression \(\left( x + \sqrt{x^{3} - 1} \right)^{5}\)+ \(\left( x - \sqrt{x^{3} - 1} \right)^{5...

The expression (x+x3−1)5\left( x + \sqrt{x^{3} - 1} \right)^{5}+ (x−x3−1)5\left( x - \sqrt{x^{3} - 1} \right)^{5} is a polynomial of degree –

A

7

B

6

C

5

D

15

Answer

7

Explanation

Solution

(a + b)5 + (a – b)5 = 2(a5 + 5C2 a3b2 + 5C4 ab4)

Hence (x+x3−1)5\left( x + \sqrt{x^{3} - 1} \right)^{5} + (x−x3−1)5\left( x - \sqrt{x^{3} - 1} \right)^{5}

2{x5 + 5C2 x3(x3 – 1) + 5C4 x(x3 – 1)2}

\ the given expression is a polynomial of degree 7.