Difference between revisions of "1966 IMO Problems/Problem 5"
(Created page with "== Problem == Solve the system of equations <math>\begin{align*}|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_1 - a_4| x_4 = 1\\ |a_2 - a_1| x_1 +|a_2 - a_3| x_3 +|a_2 - a_3| x_3 = 1\\ |...") |
(corrected problem statement) |
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Solve the system of equations | Solve the system of equations | ||
| − | <math>\begin{align*}|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_1 - a_4| x_4 = 1\\ |a_2 - a_1| x_1 +|a_2 - a_3| x_3 +|a_2 - | + | <math>\begin{align*}|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_1 - a_4| x_4 = 1\\ |a_2 - a_1| x_1 +|a_2 - a_3| x_3 +|a_2 - a_4| x_4 = 1\\ |a_3 - a_1| x_1 +|a_3 - a_2| x_2 +|a_3-a_4|x_4= 1\\ |a_4 - a_1| x_1 +|a_4 - a_2| x_2 +|a_4 - a_3| x_3 = 1\end{align*}</math> |
where <math>a_1, a_2, a_3, a_4</math> are four different real numbers. | where <math>a_1, a_2, a_3, a_4</math> are four different real numbers. | ||
Revision as of 10:28, 29 March 2012
Problem
Solve the system of equations
$\begin{align*}|a_1 - a_2| x_2 +|a_1 - a_3| x_3 +|a_1 - a_4| x_4 = 1\\ |a_2 - a_1| x_1 +|a_2 - a_3| x_3 +|a_2 - a_4| x_4 = 1\\ |a_3 - a_1| x_1 +|a_3 - a_2| x_2 +|a_3-a_4|x_4= 1\\ |a_4 - a_1| x_1 +|a_4 - a_2| x_2 +|a_4 - a_3| x_3 = 1\end{align*}$ (Error compiling LaTeX. Unknown error_msg)
where 
are four different real numbers.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1966 IMO (Problems) • Resources | ||
| Preceded by Problem 4 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 6 |
| All IMO Problems and Solutions | ||
