12.5.7 Olympic Algebra

Condition: a positive number \ (a \). It is known that the equation \ (x^{3}+1 = a x \) has exactly two positive roots, and the attitude of the larger of them to the smaller is equal to 2018. The equation \ (x^{3}+1 = a x^{2} \) also has exactly two positive roots. Prove that the attitude of more of them to smaller is also equal to 2018.