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10.8

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(2)

ratio, lines symmetric wrt line (IV Soros Olympiad 1997-98 Correspondence 10.8)

Source:

6/1/2024
In triangle ABCABC, angle BB is different from a right angle, AB:BC=kAB : BC = k. Let MM be the midpoint of ACAC. Lines symmetric to BMBM wrt ABAB and BCBC intersect line ACAC at points DD and EE. Find BD:BEBD : BE.
ratiogeometry
a root of x^3-x-1=0 (IV Soros Olympiad 1997-98 R3 10.8)

Source:

6/2/2024
Let aa be the root of the equation x3−x−1=0x^3-x-1=0. Find an equation of the third degree with integer coefficients whose root is a3a^3.
algebrapolynomial