2023 SSMO Accuracy Round Problems/Problem 3

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 $a+b+c$ .

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2023 SSMO Accuracy Round Problems/Problem 3

Problem

Solution