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2023 SSMO Accuracy Round Problems/Problem 3

Revision as of 22:21, 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...")
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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

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