MathDB

5

Part of 2018 CHMMC (Fall)

Problems(2)

2018 Fall Team #5

Source:

4/17/2022
Let △ABC\vartriangle ABC be a right triangle such that AB=3AB = 3, BC=4BC = 4, AC=5AC = 5. Let point DD be on ACAC such that the incircles of △ABD\vartriangle ABD and △BCD\vartriangle BCD are mutually tangent. Find the length of BDBD.
geometry
2018 CHMMC Tiebreaker 5 - roots of p(x) = 2x^5 - 3x^3 + 2x -7

Source:

3/2/2024
Let a,b,c,d,ea,b, c, d,e be the roots of p(x)=2x5−3x3+2x−7p(x) = 2x^5 - 3x^3 + 2x -7. Find the value of (a3−1)(b3−1)(c3−1)(d3−1)(e3−1).(a^3 - 1)(b^3 - 1)(c^3 - 1)(d^3 - 1)(e^3 - 1).
algebrapolynomialCHMMC