当x>0,y>0且√x(√x+√y)=3√y(√x+5√y),求2x+(√xy)+3y/x+(√xy)-y的值
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当x>0,y>0且√x(√x+√y)=3√y(√x+5√y),求2x+(√xy)+3y/x+(√xy)-y的值
![当x>0,y>0且√x(√x+√y)=3√y(√x+5√y),求2x+(√xy)+3y/x+(√xy)-y的值](/uploads/image/z/11541112-16-2.jpg?t=%E5%BD%93x%3E0%2Cy%3E0%E4%B8%94%E2%88%9Ax%28%E2%88%9Ax%2B%E2%88%9Ay%29%3D3%E2%88%9Ay%28%E2%88%9Ax%2B5%E2%88%9Ay%29%2C%E6%B1%822x%2B%28%E2%88%9Axy%29%2B3y%2Fx%2B%28%E2%88%9Axy%29-y%E7%9A%84%E5%80%BC)
√x(√x+√y)=3√y(√x+5√y)
x-2√xy-15y=0
(√x-5√y)(√x+3√y)=0
因为x>0,y>0
所以√x=5√y
x=25y
代入后式得到:
[2x+(√xy)+3y]/[x+(√xy)-y]
=(50y+5y+3y)/[25y+5y-y]
=2
x-2√xy-15y=0
(√x-5√y)(√x+3√y)=0
因为x>0,y>0
所以√x=5√y
x=25y
代入后式得到:
[2x+(√xy)+3y]/[x+(√xy)-y]
=(50y+5y+3y)/[25y+5y-y]
=2
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