# MIE 2015

## Contents

## Day 1

### Problem 1

Given any three sets , and . The set is equal to the set:

(a)

(b)

(c)

(d)

(e)

### Problem 2

The polynomial has real roots , and . Thus the value of the sum of is:

(a)

(b)

(c)

(d)

(e)

### Problem 3

Let and be positive integers such that . Find the remainder of the division of by .

(a)

(b)

(c)

(d)

(e)

### Problem 4

Compute

Imgcis

(a)

(b)

(c)

(d)

(e)

Note: Img(w) is the imaginary part of w.

### Problem 5

Let . It's known that and have a root in common. Therefore, we can say that for every value of and :

(a)

(b)

(c)

(d)

(e)

### Problem 6

Let be a geometric progression and , and be a arithmetic progression, both in these order, so we can say that , and :

(a) are the sides of a obtusangle triangle.

(b) are the sides of a acutangle triangle that's not equilateral.

(c) are the sides of a equilateral triangle.

(d) are the sides of a right triangle.

(e) can't be the sides of a triangle.

### Problem 7

Compute

(a)

(b)

(c)

(d)

(e)

*This article is a stub. Help us out by expanding it.*