Art of Problem Solving
Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2010 AIME II Problems/Problem 7: Difference between revisions

Newer edit →
Created page with 'set <math>w=x+yi</math>, so <math>x_1 = x+(y+3)i</math>, <math>x_2 = x+(y+9)i</math>, <math>x_3 = 2x+(2y-4)i</math>'
 
No edit summary
Line 1: Line 1:
set <math>w=x+yi</math>, so <math>x_1 = x+(y+3)i</math>, <math>x_2 = x+(y+9)i</math>, <math>x_3 = 2x+(2y-4)i</math>
set <math>w=x+yi</math>, so <math>x_1 = x+(y+3)i</math>, <math>x_2 = x+(y+9)i</math>, <math>x_3 = 2x-4+2yi</math>.
Since <math>a,b,c\in{R}</math>, the imaginary part of a,b,c must be 0.
Start with a, since it's the easiest one to do:
<math>y+3+y+9+2y=0, y=-3</math>
and therefore:
<math>x_1 = x+i</math>, <math>x_2 = x+6i</math>, <math>x_3 = 2x-4-6i</math>

Revision as of 10:51, 3 April 2010

set $w=x+yi$, so $x_1 = x+(y+3)i$, $x_2 = x+(y+9)i$, $x_3 = 2x-4+2yi$. Since $a,b,c\in{R}$, the imaginary part of a,b,c must be 0. Start with a, since it's the easiest one to do: $y+3+y+9+2y=0, y=-3$ and therefore: $x_1 = x+i$, $x_2 = x+6i$, $x_3 = 2x-4-6i$

Retrieved from "https://wiki.aopstest.com/wiki/index.php?title=2010_AIME_II_Problems/Problem_7&oldid=34183"