MathDB

3

Part of 1992 Irish Math Olympiad

Problems(2)

no of ways of choosing a pair of subsets (B,C) of A ...

Source: 1992 Irmo Paper 1 problem 3

11/21/2022
Let AA be a nonempty set with nn elements. Find the number of ways of choosing a pair of subsets (B,C)(B,C) of AA such that BB is a nonempty subset of CC.
combinatorics
complex roots

Source:

1/17/2014
Let a,b,ca, b, c and dd be real numbers with a≠0a \neq 0. Prove that if all the roots of the cubic equation
az3+bz2+cz+d=0az^{3} +bz^{2} +cz+d=0
lie to the left of the imaginary axis in the complex plane, then
ab>0,bc−ad>0,ad>0ab >0, bc-ad >0, ad>0.