xy/x+y=1/3,x^2y^2/x^2+y^2=1/5,求xy的值
来源:百度知道 编辑:UC知道 时间:2024/09/28 13:24:55
xy/(x+y)=1/3
x+y=3xy
x^y^/(x^+y^)=1/5
x^+y^=5x^y^
(x+y)^-2xy=5x^y^
(3xy)^-2xy=5x^y^
6x^y^-5x^y^-2xy=0
x^y^-2xy=0
xy(xy-2)=0
xy=0
xy=2
首先可知xy不等于0
由x²y²/(x²+y²)=1/5得:
(x²+y²)/x²y²=5
即(x²+y²+2xy-2xy)/x²y²=5
[(x+y)²-2xy]/x²y²=5
分式展开[(x+y)²/x²y²]-[2xy/x²y²]=5
因为xy/(x+y)=1/3,即(x+y)/xy=3
所以上式化为9-2/xy=5
xy=1/2
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