Difference between revisions of "1961 IMO Problems"
(→Problem 2) |
(→Problem 3) |
||
| Line 28: | Line 28: | ||
===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 10:32, 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
