作业帮∫x(∫x+2∫y)=∫y(6∫x+5∫y),求：（x+∫xy-y)/(2x+∫xy+3y)
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/05/22 01:41:54
∫x(∫x+2∫y)=∫y(6∫x+5∫y),求：（x+∫xy-y)/(2x+∫xy+3y)
因为√x(√x+2√y)=√y(6√x+5√y),
所以x+2√(xy)=6√(xy)+5y,
所以x-4√(xy)-5y=0,
所以(√x+√y)(√x-5√y)=0,
所以√x+√y=0或√x-5√y=0,
所以x=y=0或x=25y,
因为当x=y=0时,所求的式子分母为0,无意义,所以舍去;
当x=25y时,
[x+√(xy)-y]/[2x+√(xy)+3y]
=[25y+√(25y^2)-y]/[50y+√(25y^2)+3y]
=(25y+5y-y)/(50y+5y+3y)
=(29y)/(58y)
=1/2.
所以x+2√(xy)=6√(xy)+5y,
所以x-4√(xy)-5y=0,
所以(√x+√y)(√x-5√y)=0,
所以√x+√y=0或√x-5√y=0,
所以x=y=0或x=25y,
因为当x=y=0时,所求的式子分母为0,无意义,所以舍去;
当x=25y时,
[x+√(xy)-y]/[2x+√(xy)+3y]
=[25y+√(25y^2)-y]/[50y+√(25y^2)+3y]
=(25y+5y-y)/(50y+5y+3y)
=(29y)/(58y)
=1/2.
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