IOM 2016, Блиц — Задача 7

Olympiad of Metropolises, Moscow. Blitz Contest, September, 5 · 5 септември 2016 г.

Условие

Parabola $y = ax^2 + bx + c$ intersects horizontal axis at two points.

Its vertex is $A(0,2)$.

The lines $y = kx + 5$ and $y = -kx + 5$ are tangent to the parabola at $B$ and $C$ respectively.

$ABC$ is an equilateral triangle.

Find $4 \cdot (a + b + c)$.

Решение

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Оригинал в Архива: blitz.pdf