若|x-3|+|y+z|+|2z+1|=0,求XY-YZ的值

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若|x-3|+|y+z|+|2z+1|=0,求XY-YZ的值

若|x-3|+|y+z|+|2z+1|=0,求XY-YZ的值
若|x-3|+|y+z|+|2z+1|=0,求XY-YZ的值

若|x-3|+|y+z|+|2z+1|=0,求XY-YZ的值
|x-3|≥0,|y+z|≥0,|2z+1|≥0
要使|x-3|+|y+z|+|2z+1|=0成立
则有x-3=0,y+z=0,2z+1=0
求得x=3,y=1/2,z=-1/2
xy-yz=3×(1/2)-(1/2)×(-1/2)=(3/2)+(1/4)=7/4

|x-3|+|y+z|+|2z+1|=0
特殊值法
x=3,z=-1/2,y=1/2
XY-YZ=3*1/2-(-1/2)*1/2
=3/2+1/4
=7/4

因为都是绝对值 所以X-3=0 Y+2=0 2Z+1=0 X=3 Y=-2 Z=-1/2 XY=-6 YZ=1 XY-YZ=-7