Difference between revisions of "1972 IMO Problems/Problem 4"
(Created page with "==Solution== Add the five equations together to get <math>(x_1^2 - x_3 x_5)(x_2^2 - x_3 x_5) + (x_2^2 - x_4 x_1)(x_3^2 - x_4 x_1) + (x_3^2 - x_5 x_2)(x_4^2 - x_5 x_2) + (x_4^2 ...") |
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Revision as of 16:32, 17 October 2014
Solution
Add the five equations together to get
Expanding and combining, we get
Every term is , so every term must .
From the first term, we can deduce that . From the second term, . From the third term, . From the fourth term, .
Therefore, is the only solution.