设x²+(y-1)²≤4,求(x+y-1)/(x-y+3)的最值.

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设x²+(y-1)²≤4,求(x+y-1)/(x-y+3)的最值.

唔.这个题目不算简单吧.
(x+y-1)/(x-y+3)=(x-y+3+2y-2)/(x-y+3)=1+(2y-2)/(x-y+3).
接下来用换元法,另m=x-y,n=y.则题目就变成:
设 (m+n)平方+(n-1)平方《=4;求 1+2*(n-1)/(m+3).