Difference between revisions of "2013 USAJMO Problems/Problem 6"

(Solution)
(Solution)
Line 1: Line 1:
 
==Solution==
 
==Solution==
Without loss of generality, let <math>x \ge y \ge z</math>. Then <math>\sqrt{x + xyz} = \sqrt{x - 1} + \sqrt{y - 1} + \sqrt{z - 1}</math>.
+
Without loss of generality, let <math>x \le y \le z</math>. Then <math>\sqrt{x + xyz} = \sqrt{x - 1} + \sqrt{y - 1} + \sqrt{z - 1}</math>.

Revision as of 10:56, 14 April 2014

Solution

Without loss of generality, let $x \le y \le z$. Then $\sqrt{x + xyz} = \sqrt{x - 1} + \sqrt{y - 1} + \sqrt{z - 1}$.