Difference between revisions of "1961 IMO Problems"
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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 10:31, 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
