Question

Find the degree of the expression ${[x+(x^3-1{)}^{\frac{1}{2}}]}^5+{[x-(x^3-1{)}^{\frac{1}{2}}]}^5.$

Answer 1

By using Bional expansion are we get negative

terms cancels so

$[x+(x^3-1{)}^{1/2}{]}^5+[x-(x^3-1{)}^{1/2}{]}^5=$

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

$=2[x^5+10(x^6-x^3)+5(x^7+x-2x^4\left)\right]$

From above expression, degree of expression is 7.