Question

已知x+y=5,xy=3,求根号下x/y+根号下y/x的值

Answer 1

(根号下x/y+根号下y/x)^2

= x/y + y/x + 2根号下(x/y * y/x)

= (x^2+y^2)/(xy) + 2

= (x^2+2xy+y^2 - 2xy)/(xy) + 2

= (25 - 2*3)/3 + 2

= 19/3 + 2

= 25/3.