1966 IMO Problems/Problem 5
Solve the system of equations
where are four different real numbers.
Take a1 > a2 > a3 > a4. Subtracting the equation for i=2 from that for i=1 and dividing by (a1 - a2) we get:
Subtracting the equation for i=4 from that for i=3 and dividing by (a3 - a4) we get:
Hence x1 = x4. Subtracting the equation for i=3 from that for i=2 and dividing by (a2 - a3) we get:
Hence , and .
|1966 IMO (Problems) • Resources|
|1 • 2 • 3 • 4 • 5 • 6||Followed by|
|All IMO Problems and Solutions|