这两道题该怎么做,求各位帮帮忙啊
1个回答
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1 1/3-7/12+9/20-11/30+13/42-15/56
=1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=1-1/8=7/8
∵x<y<0 xz<0 ∴z>0
又|x|>|y|>|z|
∴|x+y|=-x-y, |x-y|=y-x,|y+z|=-y-z,|x-z|=z-x,|x+y+z|=-x-y-z
∴|x+y|+|x-y|-|y+z|+|x-z|-|x+y+z|=(-x-y)+(y-x)-(-y-z)+(z-x)-(-x-y-z)
=-x-y+y-x+y+z+z-x+x+y+z=-2x+2y+3z
=1+1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1+1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=1-1/8=7/8
∵x<y<0 xz<0 ∴z>0
又|x|>|y|>|z|
∴|x+y|=-x-y, |x-y|=y-x,|y+z|=-y-z,|x-z|=z-x,|x+y+z|=-x-y-z
∴|x+y|+|x-y|-|y+z|+|x-z|-|x+y+z|=(-x-y)+(y-x)-(-y-z)+(z-x)-(-x-y-z)
=-x-y+y-x+y+z+z-x+x+y+z=-2x+2y+3z
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