## 2012年2月27日 星期一

### 不等式的疑惑

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

A^2 + k >= C
k >= C - A^2

#### 5 則留言:

Marco_Dick 提到...

wahas 提到...

wahas 提到...

Sorry I am someone who just accidentally visit this page but I do not understand why k = 2018.
If k = 2018, then if x = 2.5, x^2-5x+k = (2.5)^2-5(2.5)+2018 =2011.75<2012
Why is k 2018 but not 2019?
Thanks anyway.

goose 提到...

There have been amendments in the regulations of the current Heat Event. If the correct
answer to a question is not an integer between 0 and 9999, one should pick the integer in the above
range which is closest to the correct answer. In case of an answer midway between two such
integers, round up to the larger integer. Read the instructions on the answer sheet in detail.

2018.25 is more near to 2018 instead of 2019
so....2018

(x-5/2)^2+k >= 2018.25
k >= [2018.25-(x-5/2)^2] <= 2018.25

so the discrepency