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Algebra Level 1

Given that a b c = 1 abc=1 what is the smallest value of a + b + c a+b+c ?

Note a , b , c R + a,b,c\in \Bbb R^+


The answer is 3.

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2 solutions

First we have a b c 3 = 1 \sqrt[3]{abc}=1 therefore by AM-GM a + b + c 3 1 a + b + c 3 \frac{a+b+c}3\ge1\implies a+b+c\ge\boxed3 .

If a=b=10^-n , n being very large, and c=x , then answer can also be "x"

Ninad Jadkar - 7 years ago
Hung Pham
Jun 3, 2014

it is possible that a = b = -1, and c = 1, hence, abc = 1 and a + b + c = -1. It should be given that a,b,c are positive.

Sorry about the mistake I have edited the wording!

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