Question

已知x+y=5，xy=3，求根号y分之x+根号x分之y的值

Answer 1

根号(x/y)+根号(y/x)
=(x+y)/根号(xy)
=5/根号3
＝5根号3/3

Answer 2

(根号x/y+根号y/x)^2=x/y+y/x+2=(x^2+y^2)/(xy)+2=((x+y)^2-2xy)/(xy)+2=(5^2-2*3)/3+2=19/3+2=25/3又：根号x/y+根号y/x>0所以：根号x/y+根号y/x=5/根号3