Question 194
Solve the equations
$$
a + b + c = 0, \quad a^2 + b^2 + c^2 = 1, \quad a^3 + b^3 + c^3 = 4abc
$$
for $a$, $b$, and $c$.
$$
a + b + c = 0, \quad a^2 + b^2 + c^2 = 1, \quad a^3 + b^3 + c^3 = 4abc
$$
for $a$, $b$, and $c$.
MathNet 2026 — Part 05 Question 194
Math Olympiad Vault · MathNet 2026 — Part 05