MathDB

2

Part of 2013 CHMMC (Fall)

Problems(2)

2013 Fall Team #2

Source:

3/26/2022
Two circles of radii 77 and 1717 have a distance of 2525 between their centers. What is the difference between the lengths of their common internal and external tangents (positive difference)?
geometry
2013 CHMMC Tiebreaker 2 - roots of x^4 - 3x^2 + 6x - 12 = 1

Source:

3/1/2024
Suppose the roots of x4−3x2+6x−12=1x^4 - 3x^2 + 6x - 12 = 1 are α\alpha, β\beta, γ\gamma , and δ\delta. What is the value of α+β+γδ2+α+δ+γβ2+α+β+δγ2+δ+β+γα2?\frac{\alpha+ \beta+ \gamma }{\delta^2}+\frac{\alpha+ \delta+ \gamma}{\beta^2}+\frac{\alpha+ \beta+ \delta}{\gamma^2}+\frac{\delta+ \beta+ \gamma }{\alpha^2}?
algebrapolynomialCHMMC