Question

Expand by using binomial and find the degree of polynomial
$\left(x+\sqrt{x^{3}-1}\right)^{5}+\left(x-\sqrt{x^{3}-1}\right)^{5}$ is

• A. 7
• B. 6
• C. 5
• D. 4

Answer 1

Answer: (A)

$\left(x+\sqrt{x^{3}-1}\right)^{5}+\left(x-\sqrt{x^{3}-1}\right)^{5}$
$=2\left[x^{5}+{ }^{5} C_{2} x^{3}\left(x^{3}-1\right)+{ }^{5} C_{4} x\left(x^{3}-1\right)^{2}\right]$
$=2\left[x^{5}+10 x^{3}\left(x^{3}-1\right)+5 x^{4}\left(x^{6}-2 x^{3}+1\right]\right.$
$=10 x^{7}+20 x^{6}+2 x^{5}-20 x^{4}-20 x^{3}+10 x$
$\therefore $ polynomial has degree $7$