设x=2/根号2+根号3-1,y=2/根号2+根号3+1,求xy/x+y
问题描述:
设x=2/根号2+根号3-1,y=2/根号2+根号3+1,求xy/x+y
答
x=2/根号2+根号3-1,y=2/根号2+根号3+1,
因为
x+y/xy
=1/x+1/y
=1/(2/根号2+根号3-1)+1/(2/根号2+根号3+1)
=(√2+√3-1)/2+(√2+√3+1)/2
=√2+√3
从而
xy/(x+y)=1/(√3+√2)
=√3-√2