# Difference between revisions of "1961 IMO Problems"

(→Problem 1) |
|||

Line 1: | Line 1: | ||

==Day I== | ==Day I== | ||

===Problem 1=== | ===Problem 1=== | ||

+ | (''Hungary'') | ||

+ | Solve the system of equations: | ||

− | + | <center> | |

+ | <math> | ||

+ | \begin{matrix} | ||

+ | \quad x + y + z \!\!\! &= a \; \, \\ | ||

+ | x^2 +y^2+z^2 \!\!\! &=b^2 \\ | ||

+ | \qquad \qquad xy \!\!\! &= z^2 | ||

+ | \end{matrix} | ||

+ | </math> | ||

+ | </center> | ||

+ | where <math>a </math> and <math>b </math> are constants. Give the conditions that <math>a </math> and <math>b </math> must satisfy so that <math>x, y, z </math> (the solutions of the system) are distinct positive numbers. | ||

+ | [[1961 IMO Problems/Problem 1 | Solution]] | ||

===Problem 2=== | ===Problem 2=== |

## Revision as of 10:29, 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

### Problem 3

## Day 2

### Problem 4

### Problem 5

### Problem 6