# Difference between revisions of "1961 IMO Problems"

(→Problem 1) |
(→Problem 2) |
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===Problem 2=== | ===Problem 2=== | ||

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

− | + | <math>a^2 + b^2 + c^2 \ge 4S\sqrt{3}</math> | |

+ | In what case does equality hold? | ||

+ | [[1961 IMO Problems/Problem 2 | Solution]] | ||

===Problem 3=== | ===Problem 3=== |

## Revision as of 11:31, 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

## Day 2

### Problem 4

### Problem 5

### Problem 6