Question

已知x小于0，z大于0，xy大于零，丨y丨大于丨z丨大于丨x丨，化简丨x+z丨+丨y+z丨-丨x-y丨

Answer 1

x<0,xy>0可得y<0,又已知z>0
-y>z>-x
丨x+z丨+丨y+z丨-丨x-y丨
=x+z-y-z-(x-y)
=x-y-x+y
=0

Answer 2

x<0 xy>0 y<0 z>0
丨y丨大于丨z丨大于丨x丨
y<x<0<z
丨x+z丨+丨y+z丨-丨x-y丨
=-(x+z)-(y+z)-(x-y)
=-x-z-y-z-x+y
=-2x-2z

Answer 3

由x＜0，xy＞0可知：y＜0.
又∵丨y丨＞丨z丨＞丨x丨
∴x+z＞0，y+z＜0，x-y＞0
∴丨x+z丨+丨y+z丨-丨x-y丨化简可得：
x+z+[-(y+z)]-（x-y）=0
希望对您有所帮助，欢迎再次提问。

Answer 4

x<0,z>0,xy>0,则有y<0

|y|>|z|>|x|
即有-y>z>-x
所以有:x+z>0,y+z<0,x-y>0
故原式=(x+z)-(y+z)-(x-y)=0

Answer 5

丨x+z丨+丨y+z丨-丨x-y丨
=x+z+(-y-z)-(x-y)
=x+z-y-z-x+y
=0

Answer 6

x<0,xy>0 ,y<0 且|y|>|z|>|x|那么-y>z>-x 所以x+z>0 y+z<0 x-y>0 所以
丨x+z丨+丨y+z丨-丨x-y丨=x+z-y-z-x+y=0