若x,y满足(x-1)^2+(y+2)^=4,求S=2x+y的最大值和最小值
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若x,y满足(x-1)^2+(y+2)^=4,求S=2x+y的最大值和最小值
若x,y满足(x-1)^2+(y+2)^=4,求S=2x+y的最大值和最小值
若x,y满足(x-1)^2+(y+2)^=4,求S=2x+y的最大值和最小值
可设x=2cosa+1,y=2sina-2.S=2x+y=4cosa+2sina=2√5sin(a+t)(cost=1/√5,sint=2/√5.)故Smin=-2√5,Smax=2√5.
(x-1)^2 (y+2)^2 (x-1)^2 (y+2)^2
_____ + _______=1,再令sinx=_______,cosx=_______,
4 4 4 4
再用三角函数知识解
用线性规划 或三角换元做
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