设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x-2)²+(y-1)²的取值范围

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设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x-2)²+(y-1)²的取值范围设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x

设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x-2)²+(y-1)²的取值范围
设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x-2)²+(y-1)²的取值范围

设实数x,y满足(x-y-2≤0,x+2y-5≥0,y-2≤0),u=(x-2)²+(y-1)²的取值范围
满足
{x-y-2≤0,
{x+2y-5≥0
{y-2≤0
的点P(x,y)构成的区域为
三角形ABC及其内部区域,
其中A(1,2),B(3,1),C(4,2)
令D(2,1)
则u=(x-2)²+(y-1)²=|PD|²,
|PD|min=|2*2+2-5|/√5=1/√5
|PD|max=|CD|=√[(4-2)²+(2-1)²]=√5
∴umax=5,umin=1/5
即u的范围是[1/5,5]