Question 111
Find all triples $(a, b, c)$ of real numbers satisfying
$$
a + b + c = 1 \quad \text{and} \quad 3(a + bc) = 4(b + ca) = 5(c + ab).
$$
$$
a + b + c = 1 \quad \text{and} \quad 3(a + bc) = 4(b + ca) = 5(c + ab).
$$
MathNet 2022-part-04 — 197 problems (EN–VI) Question 111
Math Olympiad Vault · MathNet 2022-part-04 — 197 problems (EN–VI)