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MathNet 2019-part-03 — 184 problems (EN–VI) Question 60

Math Olympiad Vault · MathNet 2019-part-03 — 184 problems (EN–VI)

Question 60

If $57a + 88b + 125c \ge 1148$, where $a, b, c \gt 0$, what is the minimum value of
$$
a^3 + b^3 + c^3 + 5a^2 + 5b^2 + 5c^2?
$$