Question

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

• A. $2$
• B. $-1$
• C. $0$
• D. $1$

Answer 1

The correct option is A $2$

${(x+\sqrt{x^3-1})}^5+{(x-\sqrt{x^3-1})}^5$

${}^5{c}_r{x}^{5-r}{\left(\sqrt{x^3-1}\right)}^r=$ General term

${}^5{c}_r{x}^{5-r}{(-\sqrt{x^3-1})}^r=$ General term

For degree terms

$2[{}^5{C}_0\cdot x^5+{}^5{c}_2{x}^3(x^3-1)+{}^5{c}_{4}x{(x^3-1)}^2]$

$2(x^5+10x^6-10x^3+5x^7-10x^4+5x]$

Considering only odd degree term,

$=2(1-10+5+5)$

=2 Ans

option (a)