已知:a,b,c,d,e为非零整数 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|已知:a,b,c,d,e为非零整数 且 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|a+b+c+d+e|最小值
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![已知:a,b,c,d,e为非零整数 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|已知:a,b,c,d,e为非零整数 且 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|a+b+c+d+e|最小值](/uploads/image/z/3965966-62-6.jpg?t=%E5%B7%B2%E7%9F%A5%3Aa%2Cb%2Cc%2Cd%2Ce%E4%B8%BA%E9%9D%9E%E9%9B%B6%E6%95%B4%E6%95%B0+a%2B%28b%2Bc%2Bd%2Be%29%2F2%3Db%2B%28c%2Bd%2Be%2Ba%29%2F3%3Dc%2B%28d%2Be%2Ba%2Bb%29%2F4%3Dd%2B%28e%2Ba%2Bb%2Bc%29%2F5%3De%2B%28a%2Bb%2Bc%2Bd%29%2F6+%E6%B1%82%2C%7C%E5%B7%B2%E7%9F%A5%3Aa%2Cb%2Cc%2Cd%2Ce%E4%B8%BA%E9%9D%9E%E9%9B%B6%E6%95%B4%E6%95%B0+%E4%B8%94+a%2B%28b%2Bc%2Bd%2Be%29%2F2%3Db%2B%28c%2Bd%2Be%2Ba%29%2F3%3Dc%2B%28d%2Be%2Ba%2Bb%29%2F4%3Dd%2B%28e%2Ba%2Bb%2Bc%29%2F5%3De%2B%28a%2Bb%2Bc%2Bd%29%2F6+%E6%B1%82%2C%7Ca%2Bb%2Bc%2Bd%2Be%7C%E6%9C%80%E5%B0%8F%E5%80%BC)
已知:a,b,c,d,e为非零整数 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|已知:a,b,c,d,e为非零整数 且 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|a+b+c+d+e|最小值
已知:a,b,c,d,e为非零整数 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|
已知:a,b,c,d,e为非零整数 且 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6
求,|a+b+c+d+e|最小值
已知:a,b,c,d,e为非零整数 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|已知:a,b,c,d,e为非零整数 且 a+(b+c+d+e)/2=b+(c+d+e+a)/3=c+(d+e+a+b)/4=d+(e+a+b+c)/5=e+(a+b+c+d)/6 求,|a+b+c+d+e|最小值
大概是437吧!算起来有点麻烦,但是原理还是很简单的!
设 x=(a+b+c+d+e)
然后60a+30(b+c+d+e)=60b+20(a+c+d+e)=60c+15(a+b+d+e)=60d+12(a+b+c+e)=60e+10(a+b+c+d)
30x+30a=20x+40b=15x+45c=12x+48d=10x+50e得
50e=20x+30a ==>e=(2x+3a)/5
48d=18x+30a ==>d=(3x+5a)/8
45c=15x+30a ==>c=(x+2a)/3
40b=10x+30a ==>b=(x+3a)/4
==》120(a+b+c+d+e)=48x+72a+45x+75a+40x+80a+30x+90a+120a=120x
==>a=-43x/437
c=117x/437
d=137x/437
e=149x/437
在这个题目中,由于都是比值的关系且a,b,c,d,e都是对等的,如果要是他们都是整数则x最小的值是他们的最小公倍数,就是437.
哇~~什么时候的知识啊这么难!