12.5.7 Olympic algebra

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