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HMMT 二月 2007 · 几何 · 第 1 题

HMMT February 2007 — Geometry — Problem 1

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 3 ] A cube of edge length s > 0 has the property that its surface area is equal to the sum of its volumeand five times its edge length. Compute all possible values of s .
解析

英文解析

  1. [ 3 ] A cube of edge length s > 0 has the property that its surface area is equal to the sum of its volumeand five times its edge length. Compute all possible values of s .
    3 2 2 3
    Answer: 1 , 5 . The volume of the cube is s and its surface area is 6 s , so we have 6 s = s + 5 s , or
    3 2
    0 = s − 6 s + 5 s = s ( s − 1)( s − 5).