1987 USAMO Problems/Problem 1: Difference between revisions
Bassmaster (talk | contribs) Created page with "By expanding you get <math></math>m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3<math>. From this the two m^3 cancel and you get: <cmath>2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0</cmath> You ..." |
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By expanding you get <math></math>m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3<math>. | By expanding you get <math></math>m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3<math>.</math> | ||
From this the two m^3 cancel and you get: | From this the two m^3 cancel and you get: | ||
<cmath>2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0</cmath> | <cmath>2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0</cmath> | ||
You can divide by </math> | You can divide by <math>n</math> (nonzero). | ||
You get: | You get: | ||
<cmath>2n^2+m+m^2n+3m^2-3mn=0</cmath> | <cmath>2n^2+m+m^2n+3m^2-3mn=0</cmath> | ||
Revision as of 10:15, 20 December 2015
By expanding you get $$ (Error compiling LaTeX. Unknown error_msg)m^3+mn+m^2n^2 +n^3=m^3-3m^2n+3mb^2-n^3
From this the two m^3 cancel and you get:
![\[2n^3 +mn+m^2n^2 + 3m^2n - 3mn^2=0\]](http://latex.artofproblemsolving.com/4/2/8/4280b7e66e77cbcafd88221eac9fe0f393490077.png)
You can divide by 
(nonzero).
You get:
![\[2n^2+m+m^2n+3m^2-3mn=0\]](http://latex.artofproblemsolving.com/9/8/9/98978fc9b2412fa469ad1a9a34ac576da4625162.png)
