HMMT 二月 1998 · 代数 · 第 4 题
HMMT February 1998 — Algebra — Problem 4
题目详情
英文原题
- Given that r and s are relatively prime positive integers such that = ,
5 ( ( 3 + 5 )sfind r and s .
解析
英文解析
- Problem: Given that r and s are relatively prime positive integers such that = , find r
√
5( 3+ 5)sand s .
√ √
4(12+4 5) 16(3+ 5)2
r 16
√ √
Solution: Squaring both sides of the given equation yields = = = . Because rs 252
25(3+ 5) 25(3+ 5)
and s are positive and relatively prime, then by inspection, r = 4 and s = 5 .