Difference between revisions of "2012 AMC 10A Problems/Problem 24"
(Created page with "== Problem 24 == Let <math>a</math>, <math>b</math>, and <math>c</math> be positive integers with <math>a\geb\gec</math> such that [\a^2-b^2-c^2+ab=2011]\ and [\a^2+3b^2+3c^2-3a...") |
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Let <math>a</math>, <math>b</math>, and <math>c</math> be positive integers with <math>a\geb\gec</math> such that | Let <math>a</math>, <math>b</math>, and <math>c</math> be positive integers with <math>a\geb\gec</math> such that | ||
| − | + | <math>a^2-b^2-c^2+ab=2011</math> and | |
| − | + | <math>a^2+3b^2+3c^2-3ab-2ac-2bc=-1997</math>. | |
| + | |||
| + | What is <math>a</math>? | ||
<math> \textbf{(A)}\ 249\qquad\textbf{(B)}\ 250\qquad\textbf{(C)}\ 251\qquad\textbf{(D)}\ 252\qquad\textbf{(E)}\ 253 </math> | <math> \textbf{(A)}\ 249\qquad\textbf{(B)}\ 250\qquad\textbf{(C)}\ 251\qquad\textbf{(D)}\ 252\qquad\textbf{(E)}\ 253 </math> | ||
Revision as of 20:18, 8 February 2012
Problem 24
Let 
, 
, and 
be positive integers with $a\geb\gec$ (Error compiling LaTeX. Unknown error_msg) such that
and
.
What is ?
