已知ABC是非零整数,且A+B+C=1.求证根号下3A+1+根号下3B+1+根号下3C+1小于等与3倍根号下2求过程阿
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![已知ABC是非零整数,且A+B+C=1.求证根号下3A+1+根号下3B+1+根号下3C+1小于等与3倍根号下2求过程阿](/uploads/image/z/3799367-71-7.jpg?t=%E5%B7%B2%E7%9F%A5ABC%E6%98%AF%E9%9D%9E%E9%9B%B6%E6%95%B4%E6%95%B0%2C%E4%B8%94A%2BB%2BC%3D1.%E6%B1%82%E8%AF%81%E6%A0%B9%E5%8F%B7%E4%B8%8B3A%2B1%2B%E6%A0%B9%E5%8F%B7%E4%B8%8B3B%2B1%2B%E6%A0%B9%E5%8F%B7%E4%B8%8B3C%2B1%E5%B0%8F%E4%BA%8E%E7%AD%89%E4%B8%8E3%E5%80%8D%E6%A0%B9%E5%8F%B7%E4%B8%8B2%E6%B1%82%E8%BF%87%E7%A8%8B%E9%98%BF)
已知ABC是非零整数,且A+B+C=1.求证根号下3A+1+根号下3B+1+根号下3C+1小于等与3倍根号下2求过程阿
已知ABC是非零整数,且A+B+C=1.求证根号下3A+1+根号下3B+1+根号下3C+1小于等与3倍根号下2
求过程阿
已知ABC是非零整数,且A+B+C=1.求证根号下3A+1+根号下3B+1+根号下3C+1小于等与3倍根号下2求过程阿
先证引理:a+b+c
由题易得A<1,B<1,C<1,所以3A加1<4,3B加1<4,3C加1<4=根号下2,所以得证
由不等式的性质得
根号下3A+1+根号下3B+1+根号下3C+1≤3根号(((3A+1)+(3B+1)+(3C+1)/3) =3根号[3 (A+B+C)+3]/3=3根号2