若a,b,c为整数,且|a-b|+|c-b|=1,求|a-b|+|b-c|+|c-a|的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 21:45:12
![若a,b,c为整数,且|a-b|+|c-b|=1,求|a-b|+|b-c|+|c-a|的值](/uploads/image/z/12622764-12-4.jpg?t=%E8%8B%A5a%2Cb%2Cc%E4%B8%BA%E6%95%B4%E6%95%B0%2C%E4%B8%94%7Ca-b%7C%2B%7Cc-b%7C%3D1%2C%E6%B1%82%7Ca-b%7C%2B%7Cb-c%7C%2B%7Cc-a%7C%E7%9A%84%E5%80%BC)
若a,b,c为整数,且|a-b|+|c-b|=1,求|a-b|+|b-c|+|c-a|的值
若a,b,c为整数,且|a-b|+|c-b|=1,求|a-b|+|b-c|+|c-a|的值
若a,b,c为整数,且|a-b|+|c-b|=1,求|a-b|+|b-c|+|c-a|的值
根据|a-b|+|c-b|>=|c-a|,知道|c-a|=0或1,由于|c-a=0有C=a,这时2|b|=1与a,b,c为整数矛盾,所以
|c-a|=1,|a-b|+|b-c|+|c-a|=2
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收起
因为a,b,c为整数,所以|a-b|,|c-b|为大于等于0的整数,所以|a-b|=0,|c-b|=1或|a-b|=1,|c-b|=0,即a=b,|c-b|=|c-a|=|b-c|=1或b=c,|a-b|=|a-c|=|c-a|=1