本屆初賽高中組其中一道題為:
Let k be a constant. It is given that for real number x , the minimum value of
x^2 - 5x + k is 2012. Find k.
A solution provided by one of the contestant:
x^2 - 5x + k >= 2012
(x - 5/2)^2 + k >= 2012 + 25/4
So, k >= 2018.25
k = 2019
官方答案的 k 為 2018.
大家看到問題在哪嗎?
提示:
A^2 + k >= C
k >= C - A^2