MathDB

2020 MOAA Theme Optimization TO 5

Source:

January 23, 2022

algebratheme2020

Problem Statement

For a real number

x

, the minimum value of the expression

\frac{2x^2 + x - 3}{x^2 - 2x + 3}

can be written in the form

\frac{a-\sqrt{b}}{c}

, where

a, b

, and

c

are positive integers such that

a

and

c

are relatively prime. Find

a + b + c

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