HMMT 二月 2002 · 代数 · 第 3 题
HMMT February 2002 — Algebra — Problem 3
题目详情
英文原题
- Real numbers a, b, c satisfy the equations a + b + c = 26 , 1 /a + 1 /b + 1 /c = 28. Find the value ofa b c a c b + + + + + .
b c a c b a
解析
英文解析
- Real numbers a, b, c satisfy the equations a + b + c = 26 , 1 /a + 1 /b + 1 /c = 28. Findthe value ofa b c a c b + + + + + .
b c a c b a
Solution: 725 Multiplying the two given equations givesa a a b b b c c c + + + + + + + + = 26 · 28 = 728 ,
a b c a b c a b cand subtracting 3 from both sides gives the answer, 725.