Question

高一数学！！！！！

若x,y满足(x-1)^2+(y+2)^2=5，则x-2y的最大值是？

Answer 1

解:
由于
(x-1)^2+(y+2)^2=5

则:
[(x-1)^2/5]+[(y+2)^2/5]=1
[(x-1)/根号5]^2+[(y+2)/根号5]^2=1

则设:
sina=(x-1)/根号5
cosa=(y+2)/根号5

则:
x=根号5sina+1
y=根号5cosa-2

则:
x-2y
=[根号5sina+1]-2*[根号5cosa-2]
=根号5(sina-2cosa)+5
=根号5*[根号5sin(a-w)]+5
=5sin(a-w)+5

由于sin(a-w)属于[-1,1]
则:当sin(a-w)=1时
x-2y取最大值=10

Answer 2

x,y满足(x-1)^2+(y+2)^2=5
x-2y取最大值=10

Answer 3