HMMT 十一月 2017 · 冲刺赛 · 第 1 题
HMMT November 2017 — Guts Round — Problem 1
题目详情
(1) Some ball has been drawn at least twelve times (not necessarily consecutively).
解析
- [ 2 ] Suppose x is a rational number such that x 2 is also rational. Find x . Proposed by: Michael Kural Answer: 0 √ √ x 2 Suppose x 6 = 0. Then = 2 is the quotient of two nonzero rationals, and so is rational. However, x √ it is well-known that 2 is irrational. Therefore any solution x must satisfy x = 0. We can see that 0 √ is rational and 0 2 = 0 is rational, so the answer is indeed x = 0 .