MathDB

2023 MOAA Accuracy P5

Source:

October 13, 2023

MOAA 2023

Problem Statement

Let

k

be a constant such that exactly three real values of

x

satisfy

x-|x^2-4x+3| = k

The sum of all possible values of

k

can be expressed in the form

\frac{m}{n}

where

m

and

n

are relatively prime positive integers, find

m+n

.
Proposed by Andy Xu