Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2023 SSMO Accuracy Round Problems/Problem 3

Revision as of 21:21, 15 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Suppose that <math>a, b, c</math> are real numbers such <cmath> \begin{align*} a + b - c &= 4 \\ a^2 + b^2 + c^2 &= 14 \\ a^3 + b^3 - c^3 &= 34 \\ \end...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Suppose that $a, b, c$ are real numbers such \begin{align*} a + b - c &= 4 \\ a^2 + b^2 + c^2 &= 14 \\ a^3 + b^3 - c^3 &= 34 \\ \end{align*} Find the sum of all possible values of $a+b+c$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_SSMO_Accuracy_Round_Problems/Problem_3&oldid=207649"