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Cauchy Help!

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Let $$a,b,c$$   be positive real numbers such that $$a + b + c = 1$$. Find the minimum value of

$$\frac{1}{a + 2b} + \frac{1}{b + 2c} + \frac{1}{c + 2a}.$$

Jan 7, 2022

#1
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The minimum value is 3/4.

Jan 7, 2022
#2
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I believe it is 3....

because 1/3/4 is equal to 4/3, which is greater than one....

I'm pretty shure I am wrong so @guest can you give an explanation?

Jan 7, 2022