2024 SSMO Relay Round 4 Problems/Problem 3

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