Difference between revisions of "2010 AIME II Problems/Problem 7"
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<math>y+3+y+9+2y=0, y=-3</math> | <math>y+3+y+9+2y=0, y=-3</math> | ||
and therefore: | and therefore: | ||
| − | <math>x_1 = x | + | <math>x_1 = x</math>, <math>x_2 = x+6i</math>, <math>x_3 = 2x-4-6i</math> |
| + | 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, <math>x_1 = 4, x_2 = 4+6i, x_3 = 4-6i</math> | ||
Revision as of 11:56, 3 April 2010
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, 
