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• 2012 AMC 12A Problems/Problem 18
  ...math>. On the other hand the area is given by <math>(1/2)25r+(1/2)26r+(1/2)27r</math>. Then <math>39r=\sqrt{39(14)(13)(12)}</math> so that <math>r^2=56</
  4 KB (717 words) - 19:07, 28 July 2021
• 2024 AIME I Problems/Problem 15
  ...sion, we get <cmath>(x^2 + (r - m)x + (27 + r^2 - rm) + \frac{r^3 - r^2m + 27r - 23}{x - r})(x - r) = x^3 - mx^2 + 27x - 23</cmath>Since we defined r to b <math>r^3-r^2m+27r-23=0</math> or <math>m = r + \frac{27}{r} - \frac{23}{r^2}</math>
  15 KB (2,475 words) - 23:18, 31 July 2024