Algebra Answers

Give a direct proof, as well as a proof by contradiction, of the following statement:
A intersection B is contained in A union B for any two sets A and B.

Find the polynomial equation over R of lowest degree which is satisfied by (1-i) and (3+2i).

Apply Cardano's method for finding the roots of 2x^3+3x^2-8x-12=0.

Use weirstrass' inequalities to prove that
Summation of i=1 to n (1/√i) <= (1/√n! ) Summation of i=2 (√(i-1) )+ 2* summation of i=2 to n (1/√i)

prove that (a union b)\(a intersection b)= (a\b) union (b\a) for any two sets a and b in a universal set u.

prove that 2^n > 1+n*√2^(n-1) for all n>2

let A= {x€z| x is a multiple of 5} and B={x€z | x is a divisor of 20} . Represent A,B and A' intersection B by the listing method and in a Venn diagram.

Give three numbers between negative 5 and 8 that satisfy the given condition.
Real​ numbers, but not rational numbers.
Select all that apply.

A bag contains red and green marbles. For every 5 marbles Jackie picks, at least 1 marble is red. For every 6 marbles Jackie picks, at least 1 marble is green. What is the largest number of marbles that the bag can contain?

Monica has to choose 5 different numbers. She has to multiply some of them by 2 and some by 3 in order to get the smallest number of different results. What is the least number of results she can obtain?