题目内容
若实数x,y满足则x2-2xy+y2的取值范围是( )
A.[0,4] | B.[0,] |
C.[4,] | D.[0,] |
B
将x2-2xy+y2变形为(x-y)2,只需求出x-y的取值范围即可得到(x-y)2的取值范围.
画出可行域(如图),
x2-2xy+y2=(x-y)2,令z=x-y,则y=x-z,可知当直线y=x-z经过点M(-,3)时z取最小值zmin=-;当直线y=x-z经过点P(5,3)时z取最大值zmax=2,即-≤z=x-y≤2,所以0≤x2-2xy+y2≤.
画出可行域(如图),
x2-2xy+y2=(x-y)2,令z=x-y,则y=x-z,可知当直线y=x-z经过点M(-,3)时z取最小值zmin=-;当直线y=x-z经过点P(5,3)时z取最大值zmax=2,即-≤z=x-y≤2,所以0≤x2-2xy+y2≤.
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