Difference between revisions of "1970 Canadian MO Problems/Problem 1"
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Revision as of 21:39, 14 December 2011
Problem
Find all number triples such that when any of these numbers is added to the product of the other two, the result is
.
Solution
We have:
From the first equation minus the second, we get :
So either or
. For
, since the equations were symmetric, we have one solution of
.
From
, substituting it into the original three derived equations, we have:
We then get
Substituting this into
,
Thus, either
, or
. Since the equations were symmetric, we then get the full solution set of:
1970 Canadian MO (Problems) | ||
Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 2 |