# Difference between revisions of "2012 AMC 10A Problems/Problem 24"

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== Problem 24 == | == Problem 24 == | ||

− | Let <math>a</math>, <math>b</math>, and <math>c</math> be positive integers with <math>a\ | + | Let <math>a</math>, <math>b</math>, and <math>c</math> be positive integers with <math>a\ge</math> <math>b\ge</math> <math>c</math> such that |

<math>a^2-b^2-c^2+ab=2011</math> and | <math>a^2-b^2-c^2+ab=2011</math> and | ||

<math>a^2+3b^2+3c^2-3ab-2ac-2bc=-1997</math>. | <math>a^2+3b^2+3c^2-3ab-2ac-2bc=-1997</math>. |

## Revision as of 20:43, 8 February 2012

## Problem 24

Let , , and be positive integers with such that and .

What is ?