x比y=根号2比根号3,则xy分之(x-y)的平方=

题目

x比y=根号2比根号3,则xy分之(x-y)的平方=

答案

x:y=√2:√3
∴x/y=√6/3,y/x=√6/2
(x-y)²/(xy)
=(x²-2xy+y²)/(xy)
=x²/(xy)-2+y²/(xy)
=x/y+y/x-2
=√6/3+√6/2-2
=5√6/6 -2