1999 JBMO Problems/Problem 1
Problem
Let be five real numbers such that , and . If are all distinct numbers prove that their sum is zero.
Solution
After solving for in all three equations, we have Thus, we know that .
Since , rearrange and factor terms to get
Since , . By using the same steps, , so by substituting and rearranging terms, we have
Since , we must have .
See Also
1999 JBMO (Problems • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |