MathDB

13

Part of 2014 ASDAN Math Tournament

Problems(2)

2014 General #13

Source:

7/5/2022
Square S1S_1 is inscribed inside circle C1C_1, which is inscribed inside square S2S_2, which is inscribed inside circle C2C_2, which is inscribed inside square S3S_3, which is inscribed inside circle C3C_3, which is inscribed inside square S4S_4.

Let aa be the side length of S4S_4, and let bb be the side length of S1S_1. What is ab\tfrac{a}{b}?
2014General Test
2014 Team #13

Source:

7/1/2022
Let α,β,γ\alpha,\beta,\gamma be the three real roots of the polynomial x3−x2−2x+1=0x^3-x^2-2x+1=0. Find all possible values of αβ+βγ+γα\tfrac{\alpha}{\beta}+\tfrac{\beta}{\gamma}+\tfrac{\gamma}{\alpha}.
2014team test