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

2024 SSMO Relay Round 4 Problems/Problem 3

Revision as of 16:02, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> Given that: \begin{align*} a+b &= -c,\\ a^3 - abc &= 4,\text{ and }\\ b^3 - abc &= T.\\ \end{align*} Then, <math>abc - c^3 = x.</math>...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $T = TNYWR.$ Given that: \begin{align*} a+b &= -c,\\ a^3 - abc &= 4,\text{ and }\\ b^3 - abc &= T.\\ \end{align*} Then, $abc - c^3 = x.$ Find the value of $x.$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2024_SSMO_Relay_Round_4_Problems/Problem_3&oldid=247959"