Answer:
[tex](\sqrt{x})^{5}(5/x)^{4}[/tex]
Step-by-step explanation:
Hi there.
Well, let's translate it from Latex. Then expanding it:
[tex]\left(\sqrt{x}+\dfrac5x\right)^{9}=[/tex] [tex](\sqrt{x})^9(5/x)^{0} +(\sqrt{x})^{8}(5/x)^{1}+(\sqrt{x})^{7}(5/x)^{2} \\+(\sqrt{x})^{6}(5/x)^{3}+(\sqrt{x})^{5}(5/x)^{4}+(\sqrt{x})^{4}(5/x)^{5}\\+(\sqrt{x})^{3}(5/x)^{6}+(\sqrt{x})^{2}(5/x)^{7}+(\sqrt{x})^{1}(5/x)^{8}+(\sqrt{x})^{0}(5/x)^{9} =[/tex]
[tex]\frac{\left(5+x^{\frac{3}{2}}\right)^9}{x^9}[/tex]
Finding a constant term, in a Binomial has its cases.
In this case, there's no constant as a real number. Also, this an univariate binomial. So to find this Binomial expansion's constant term. We must follow this formula, (for a 9th degree) there are 10 terms:
[tex]n-2k=0\\10 -2k =0\\K=5th :\term\\[/tex]
[tex](\sqrt{x})^{5}(5/x)^{4}[/tex]
Because this result satisfy a ratio.
[tex]y=\frac{c}{x}[/tex]
Where c is the constant term, x is the first term of this binomial
