Difference between revisions of "1959 IMO Problems/Problem 2"
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− | given (a) <math>A=\sqrt{2}</math>, (b) <math>A=1</math>, (c) <math>A=2</math>, | + | given (a) <math>A=\sqrt{2}</math>, (b) <math>A=1</math>, (c) <math>A=2</math>, where only non-negative real numbers are admitted for square roots? |
== Solution == | == Solution == |
Revision as of 18:13, 8 June 2008
Problem
For what real values of is
given (a) , (b)
, (c)
, where only non-negative real numbers are admitted for square roots?
Solution
We note that the square roots imply that . We now square both sides and simplify to obtain
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.
1959 IMO (Problems) • Resources | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
All IMO Problems and Solutions |