1.设有比例式:x/(y+z)=y/(x+z)=z/(x+y),有比例性质,得x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=0.5x/(y+z)=y/(x+z)=(x-y)/[(y+z)-(x+z)]=-1,由此可得0.5=-1试分析推理产生错误的原因

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1.设有比例式:x/(y+z)=y/(x+z)=z/(x+y),有比例性质,得x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=0.5x/(y+z

1.设有比例式:x/(y+z)=y/(x+z)=z/(x+y),有比例性质,得x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=0.5x/(y+z)=y/(x+z)=(x-y)/[(y+z)-(x+z)]=-1,由此可得0.5=-1试分析推理产生错误的原因
1.设有比例式:x/(y+z)=y/(x+z)=z/(x+y),有比例性质,得x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=0.5
x/(y+z)=y/(x+z)=(x-y)/[(y+z)-(x+z)]=-1,由此可得0.5=-1
试分析推理产生错误的原因

1.设有比例式:x/(y+z)=y/(x+z)=z/(x+y),有比例性质,得x/(y+z)=y/(x+z)=z/(x+y)=(x+y+z)/[(y+z)+(x+z)+(x+y)]=0.5x/(y+z)=y/(x+z)=(x-y)/[(y+z)-(x+z)]=-1,由此可得0.5=-1试分析推理产生错误的原因
此处应用的是和比定理,但该定理的使用条件是分子(或分母)相加后不能等于零,例如说2=2/1=(-2)/(-1)=(2-2)/(1-1)=0/0就显然部队了.此题中在不确定x-y是否等于0的情况下用和比定理就会造成错误.

由已知,只能得到y+z,z+x,x+y均不等于0,而无法判断x+y+z和y-x到底等不等于0,所以不能利用这样的性质。