---

Problem 356

---

Largest roots of cubic polynomials

Let a_n be the largest real root of a polynomial g(x) = x³ - 2ⁿ·x² + n.
For example, a₂ = 3.86619826…

Find the last eight digits of $\sum _{i=1}^{30}\lfloor a_i^{987654321}\rfloor$.

Note: $\lfloor a\rfloor$ represents the floor function.

---

三次多项式的最大根

记a_n为多项式g(x) = x³ - 2ⁿ·x² + n的最大实根。
例如，a₂ = 3.86619826…

求$\sum _{i=1}^{30}\lfloor a_i^{987654321}\rfloor$的最后8位数字。

注：$\lfloor a\rfloor$表示下取整函数。

---