Question

The sum of the coefficients of all odd degree terms in the expansion of ${(x+\sqrt{x^3-1})}^5+{(x-\sqrt{x^3-1})}^5$ $,(x>1)$ is

• A. $1$
• B. $0$
• C. $-1$
• D. $2$

Answer 1

The correct option is D $2$

$=2({}^5{C}_0{x}^5+{}^5{C}_2{x}^3(x^3-1)+{}^5{C}_{4}x(x^3-1{)}^2)$
$=2(x^5+10(x^6-x^3)+5(x\left)\right(x^6+1-2x^3\left)\right)$
Sum of coefficients of odd powers $=2(1-10+10)=2$