Question

已知x+y=5,xy=3,求根号下x/y+根号下y/x的值=5√3/3还是= 25/3.

Answer 1

√(x/y)+√(y/x)
=√(xy)/y+√(xy)/x
=√(xy)*(x+y)/(xy)
=√3*5/3
=5√3/3

追问

(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.
这个错在哪了？

追答

没错,你算的是平方
还需要开方
原式=√(25/3)=5/√3=5*√3/(√3*√3)=5√3/3