神马品牌网苹果6plus壁纸高清:初中奥数难题,高手请进!!!!
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(1)方程17[x]=92{x}共有____组解.
(2)证明:对任意正整数n,有[n\3]+[(n+2)\6]+[(n+4)\6]=[n\2]+[(n+3)\6]
请加上详细的解题过程!
非常感谢!!
(2)证明:对任意正整数n,有[n\3]+[(n+2)\6]+[(n+4)\6]=[n\2]+[(n+3)\6]
请加上详细的解题过程!
非常感谢!!
1.17[x]=92{x}<92 =>[x]<6,
So x=85/92, 68/92,51/92,34/92,17/92,0
2. you can consider the following famous formula:
[x]+[x+1/n]+[x+2/n]+...+[x+(n-1)/n]=[nx]
where n is an integer, and x is a real number.
Then
[n\3]+[(n+2)\6]+[(n+4)\6]
=[n/3]-[n/6]+([n/6]+[(n+2)\6]+[(n+4)\6])
=[n/3]-[n/6]+[3*n/6]
=[n/3]-[n/6]+[n/2]
=[2n/6]-[n/6]+[n/2]
=[n/6+1/2]+[n/2]
=[(n+3)/6]+[n/2]