Difference between revisions of "1961 IMO Problems"
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==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
