HMMT 二月 2000 · GEN 赛 · 第 1 题
HMMT February 2000 — GEN Round — Problem 1
题目详情
- If a = 2 b + , b = 2 + d , 2 = d + a 1, d = a , what is b ? 9 Æ Æ
解析
- Sin e d = a , substitute in to the equation b = 2 + d to get b = 2 + a = a + . Also, substitute in to 2 = d + a 1 to get 2 = a + a 1, or 3 = 2 a 1. No w, sin e b = a + , w e an substitute in to a = 2 b + to get a = 2 a + 2 + , or a = 3 . Sin e w e 1 kno w 3 = 2 a 1 from ab o v e, w e substitute in to get 3 = 6 1, or = . Th us, 9 2 1 4 w e nd that a = , d = , and b = . 3 9 9 9 4