Difference between revisions of "1969 Canadian MO Problems/Problem 3"
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Revision as of 01:54, 28 July 2006
Problem
Let be the length of the hypotenuse of a right angle triangle whose two other sides have lengths and . Prove that . When does the equality hold?
Solution
Since are all positive, squaring preserves the inequality;
By the Pythagorean Theorem, since the square of a real number is always positive.