Объяснение:

[tex](\sqrt{x} +\frac{1}{x})^6.\\ C^{n-2}_n(\sqrt{x} )^{n-4}*(\frac{1}{x})^{n-2}=C^{6-2}_6*x*(\frac{1}{x})^{6-2}=C^4_6*x*(\frac{1}{x})^4= \frac{6!}{(6-4)!*4!}*\frac{x}{x^4}=\\ =\frac{4!*5*6}{2!*4!}*\frac{1}{x^3}=\frac{5*6}{1*2} *\frac{1}{x^3} =\frac{15}{x^3}.\\ \frac{15}{x^3}=\frac{5}{9}\ |:5\\ \frac{3}{x^3}=\frac{1}{9} \\ x^3=27\\ x^3=3^3\\ x=3.[/tex]

Ответ: x=3.