1959 IMO Problems/Problem 2
Problem
For what real values of is
given (a) , (b) , (c) , where only non-negative real numbers are admitted for square roots?
Solution
Firstly, the square roots imply that a valid domain for x is .
Square both sides of the given equation: and simplify to obtain
Add the first and the last terms to get
If , then we must clearly have . Otherwise, we have
Hence for (a) the solution is , for (b) there is no solution, since we must have , and for (c), the only solution is . Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
See Also
1959 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |