已知xy/x+y=1/3,x2y2/x2+y2=1/5,求xy的值.
问题描述:
已知xy/x+y=1/3,x2y2/x2+y2=1/5,求xy的值.
答
xy/x+y=1/3x+y=3xyx2y2/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]=1/55(xy)²=9(xy)²-2xy4(xy)²=2xy2xy=1xy=1/2