已知xy/x+y=1/3,x2y2/x2+y2=1/5,求xy的值.
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已知xy/x+y=1/3,x2y2/x2+y2=1/5,求xy的值.
xy/x+y=1/3
x+y=3xy
x2y2/x2+y2=1/5
(xy)²/[(x+y)²-2xy]=1/5
(xy)²/[(3xy)²-2xy]=1/5
(xy)²/[9(xy)²-2xy]=1/5
5(xy)²=9(xy)²-2xy
4(xy)²=2xy
2xy=1
xy=1/2
x+y=3xy
x2y2/x2+y2=1/5
(xy)²/[(x+y)²-2xy]=1/5
(xy)²/[(3xy)²-2xy]=1/5
(xy)²/[9(xy)²-2xy]=1/5
5(xy)²=9(xy)²-2xy
4(xy)²=2xy
2xy=1
xy=1/2
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