Question

Please help me solve this​

Answer 1

Answer: x = 16/17; y = 1/17

condition: x,y > 0

we have:

`\left \{ {{\sqrt{(x)/(y) } =4} \atop {(1)/(x)+(1)/(y)=(1)/(xy) }} \right. \\\\<=>\left \{ {{(x)/(y) =16} \atop {(1)/(x)+(1)/(y) =(1)/(xy) }} \right.`

because x > 0, multiply x by the second equation, we have:

`\left \{ {{(x)/(y) =16} \atop {x((1)/(y)+(1)/(x)) =(x)/(xy) }} \right. \\\\<=>\left \{ {{(x)/(y) =16} \atop {(x)/(y) +1=(1)/(y) }} \right.\\\\<=>\left \{ {{(x)/(y) +1=17} \atop {(x)/(y) +1=(1)/(y) }} \right.\\\\=>\left \{ {{17-(1)/(y) =0} \atop {(x)/(y) =16}} \right.\\\\<=>\left \{ {{(1)/(y) =17} \atop {x=16y}} \right.\\\\<=>\left \{ {{y=(1)/(17) } \atop {x=(16)/(17) }} \right.`

Explanation: