1.已知X、Y、Z、是3个非负数,满足3x+2y+z=5,x+y-z

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1.已知X、Y、Z、是3个非负数,满足3x+2y+z=5,x+y-z
=2.若S=2x+y-z,则S的最大值和最小值为____?
2.xy+x+y+7=0,3x+3y=9+2xy,求x^2+xy^2的值.

(1)
x+y-z=2.
y-z=2-x
所以S=2X+Y-Z=X+2
3x+2y+z=5,
x+y-z=2.
两个式子加起来4X+3Y=7 X=(7-3Y)/4
Y≥0所以0≤X≤1
所以2≤S≤3
2、
{xy+x+y+7=0 (1)
{3x+3y=9+2xy(2)
由(1)得
x+y=-7-xy
代入（2）
3(-7-xy)=9+2xy
-21-3xy=9+2xy
5xy=-30
xy=-6
那么x+y=-7-(-6)=-1
{xy=-6
{x+y=-1
解得x=-3 y=2
x^2+xy^2=(-3)²+(-3)*2²=9-12=-3

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