求问一道CXD数学题

nanlisusan

The pages of a report are numbered consecutively from 1 to 10. If the sum of the page numbers up to and including page number x of the report is equal to one more than the sum of the page numbers following page number x, then x =

A. 4
B. 5
C. 6
D. 7
E. 8

求问这道题的解法，看了解析但还是看不懂

andizza

就是1+2+3+...+x = (x+1)+(x+2)+...+10+1
(1+x)*x/2=(10+x+1)*(10-x-1+1)/2+1
整理一下
x(x+1)=(11+x)(10-x)+2 => x^2+x-56=0 => (x+8)(x-7)=0
因为x>0，所以x=7。
验算一下，1加到7是28，8加到10是27，恰好差1，满足条件。