An algebra problem by Bryan Lee Shi Yang

Algebra Level 3

Let α \alpha be the positive real root of x 2 3 x 1 = 0 x^{2} - 3x - 1 = 0 . Determine α 3 2 α 2 + 1 \lfloor \alpha^3 - 2\alpha^2 + 1 \rfloor .

Source: W M T C 2016 WMTC 2016


The answer is 15.

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