若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?xy/(x+2y-2)

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若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?xy/(x+2y-2)若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?xy/(x+2y-2)若实数x

若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?xy/(x+2y-2)
若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?
xy/(x+2y-2)

若实数x,y满足x^2+4y^2=4,则xy/x+2y-2的最大值为多少?xy/(x+2y-2)
xy/x+2y-2?
详细点啊,

答:
实数x和y满足x^2+4y^2=4
x^2/4+y^2=1,为焦点在x轴的椭圆
设x=2cost,y=sint,则:
xy/(x+2y-2)
=2sintcost/(2cost+2sint-2)
=sin2t/[2√2sin(t+45°)-2]
当2√2sin(t+45°)-2趋于0时,为无穷大
因此,不存在最大值我补充了,谢谢...

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答:
实数x和y满足x^2+4y^2=4
x^2/4+y^2=1,为焦点在x轴的椭圆
设x=2cost,y=sint,则:
xy/(x+2y-2)
=2sintcost/(2cost+2sint-2)
=sin2t/[2√2sin(t+45°)-2]
当2√2sin(t+45°)-2趋于0时,为无穷大
因此,不存在最大值

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