2010 AIME II Problems/Problem 7
Revision as of 11:58, 3 April 2010 by Sinkokuyou (talk | contribs)
set , so
,
,
.
Since
, the imaginary part of a,b,c must be 0.
Start with a, since it's the easiest one to do:
and therefore:
,
,
now, do the part where the imaginery part of c is 0, since it's the second easiest one to do:
x(x+6i)(2x-4-6i), the imaginery part is: 6x^2-24x, which is 0, and therefore x=4, since x=0 don't work,
so now,
and therefore:
, and finally, we have |a+b+c|=|-12+84-208|=136.