已知xyz满足|3x-2y+z|+|2x+y+2z|=0(xyz不等于o)求x+y除以z
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已知xyz满足|3x-2y+z|+|2x+y+2z|=0(xyz不等于o)求x+y除以z
由|3x-2y+z|≥0,|2x+y+2z|≥0,且|3x-2y+z|+|2x+y+2z|=0,得
|3x-2y+z|=|2x+y+2z|=0
∴ 3x-2y+z=2x+y+2z=0
由3x-2y+z=2x+y+2z,得x=3y+z
3x-2y+z=0,则6x-4y+2z=0,由2x+y+2z=0,两式相减得4x-5y=0,即x=(5/4)y
∴ 3y+z=(5/4)y
∴ z=-(7/4)y
∴ (x+y)/z=(3y+z+y)/z=(3y-7/4*y+y)/(-7/4)y=(9/4*y)/(-7/4)*y=-9/7
|3x-2y+z|=|2x+y+2z|=0
∴ 3x-2y+z=2x+y+2z=0
由3x-2y+z=2x+y+2z,得x=3y+z
3x-2y+z=0,则6x-4y+2z=0,由2x+y+2z=0,两式相减得4x-5y=0,即x=(5/4)y
∴ 3y+z=(5/4)y
∴ z=-(7/4)y
∴ (x+y)/z=(3y+z+y)/z=(3y-7/4*y+y)/(-7/4)y=(9/4*y)/(-7/4)*y=-9/7
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