已知整数x、y满足:1 xy 100,且 x√y + y√x - √2009x - √2009y + √2009xy = 2009 则√x+y+10的值是多就这个y x 2009x 2009y 2009xy x+y+10 均在根号下
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![已知整数x、y满足:1 xy 100,且 x√y + y√x - √2009x - √2009y + √2009xy = 2009 则√x+y+10的值是多就这个y x 2009x 2009y 2009xy x+y+10 均在根号下](/uploads/image/z/1344084-60-4.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B4%E6%95%B0x%E3%80%81y%E6%BB%A1%E8%B6%B3%EF%BC%9A1+xy+100%2C%E4%B8%94+x%E2%88%9Ay+%2B+y%E2%88%9Ax+-+%E2%88%9A2009x+-+%E2%88%9A2009y+%2B+%E2%88%9A2009xy+%3D+2009+%E5%88%99%E2%88%9Ax%2By%2B10%E7%9A%84%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%B1%E8%BF%99%E4%B8%AAy+x+2009x+2009y+2009xy+x%2By%2B10+%E5%9D%87%E5%9C%A8%E6%A0%B9%E5%8F%B7%E4%B8%8B)
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已知整数x、y满足:1 xy 100,且 x√y + y√x - √2009x - √2009y + √2009xy = 2009 则√x+y+10的值是多就这个y x 2009x 2009y 2009xy x+y+10 均在根号下
已知整数x、y满足:1 xy 100,且 x√y + y√x - √2009x - √2009y + √2009xy = 2009 则√x+y+10的值是多
就这个
y x 2009x 2009y 2009xy x+y+10 均在根号下
已知整数x、y满足:1 xy 100,且 x√y + y√x - √2009x - √2009y + √2009xy = 2009 则√x+y+10的值是多就这个y x 2009x 2009y 2009xy x+y+10 均在根号下
移项得到√xy(√x+√y+√2009)=√2009(√x+√y+√2009)
得到xy=2009,根据条件可以得到x,y分别为41,49
所以√x+y+10=10