# Difference between revisions of "1961 IMO Problems"

(→Problem 2) |
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===Problem 3=== | ===Problem 3=== | ||

+ | Solve the equation | ||

− | + | <math>\cos^n{x} - \sin^n{x} = 1</math> | |

+ | where ''n'' is a given positive integer. | ||

+ | [[1961 IMO Problems/Problem 3 | Solution]] | ||

==Day 2== | ==Day 2== |

## Revision as of 11:32, 12 October 2007

## Contents

## Day I

### Problem 1

(*Hungary*)
Solve the system of equations:

where and are constants. Give the conditions that and must satisfy so that (the solutions of the system) are distinct positive numbers.

### Problem 2

Let *a*,*b*, and *c* be the lengths of a triangle whose area is *S*. Prove that

In what case does equality hold?

### Problem 3

Solve the equation

where *n* is a given positive integer.

## Day 2

### Problem 4

### Problem 5

### Problem 6