Answer: x = 16/17; y = 1/17
condition: x,y > 0
we have:
[tex]\left \{ {{\sqrt{\frac{x}{y} } =4} \atop {\frac{1}{x}+\frac{1}{y}=\frac{1}{xy} }} \right. \\\\<=>\left \{ {{\frac{x}{y} =16} \atop {\frac{1}{x}+\frac{1}{y} =\frac{1}{xy} }} \right.[/tex]
because x > 0, multiply x by the second equation, we have:
[tex]\left \{ {{\frac{x}{y} =16} \atop {x(\frac{1}{y}+\frac{1}{x}) =\frac{x}{xy} }} \right. \\\\<=>\left \{ {{\frac{x}{y} =16} \atop {\frac{x}{y} +1=\frac{1}{y} }} \right.\\\\<=>\left \{ {{\frac{x}{y} +1=17} \atop {\frac{x}{y} +1=\frac{1}{y} }} \right.\\\\=>\left \{ {{17-\frac{1}{y} =0} \atop {\frac{x}{y} =16}} \right.\\\\<=>\left \{ {{\frac{1}{y} =17} \atop {x=16y}} \right.\\\\<=>\left \{ {{y=\frac{1}{17} } \atop {x=\frac{16}{17} }} \right.[/tex]
Step-by-step explanation:
