Art of Problem Solving

AoPS Online

2022 SSMO Tiebreaker Round Problems/Problem 2

Revision as of 19:42, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>P(x) = x^3 - 7x^2 + 9x - 2</math>. If <math>P(x) = (x - a)^3 + b(x - a) + c</math> where <math>a, b, c</math> are real numbers, then the value of <math>a...")

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $P(x) = x^3 - 7x^2 + 9x - 2$ . If $P(x) = (x - a)^3 + b(x - a) + c$ where $a, b, c$ are real numbers, then the value of $a - b - c$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$ . Find $m + n$ .

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_SSMO_Tiebreaker_Round_Problems/Problem_2&oldid=207595"

© 2024 AoPS Incorporated