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设x=2/根号2+根号3-1,y=2/根号2+根号3+1,求xy/x+y
题目详情
设x=2/根号2+根号3-1,y=2/根号2+根号3+1,求xy/x+y
▼优质解答
答案和解析
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
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
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