ta có : \(A=\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{xy}}=\dfrac{\sqrt{x}+\sqrt{y}}{\sqrt{\dfrac{1}{36}}}=\dfrac{\sqrt{x}+\sqrt{y}}{\dfrac{1}{6}}=5\)
\(\Rightarrow\sqrt{x}+\sqrt{y}=5.\dfrac{1}{6}=\dfrac{5}{6}\)
\(\Rightarrow\sqrt{x};\sqrt{y}\) là nghiệm của phương trình \(X^2-\dfrac{5}{6}X+\dfrac{1}{36}=0\)
\(\Leftrightarrow36X^2-30X+1=0\)
\(\Delta'=\left(-15\right)^2-36.1=225-36=189>0\)
\(\Rightarrow\) phương trình có 2 nghiệm phân biệt
\(X_1=\dfrac{15-\sqrt{189}}{36}=\dfrac{5-\sqrt{21}}{12}\)
\(X_2=\dfrac{15+\sqrt{189}}{36}=\dfrac{5+\sqrt{21}}{12}\)
\(X=\sqrt{x}=\dfrac{5-\sqrt{21}}{12}\Rightarrow x;y=\left(\dfrac{5-\sqrt{21}}{12}\right)^2\)
\(X=\sqrt{x}=\dfrac{5-\sqrt{21}}{12}\Rightarrow x;y=\left(\dfrac{5+\sqrt{21}}{12}\right)^2\)
