- #1

Kolmin

- 66

- 0

## Homework Statement

Let ##a## and ##b## real numbers such that ##a>b>0##.

Determine the least possible value of ##a+ \frac{1}{b(a-b)}##

I took this example from page 3 of this paper

## Homework Equations

In the article previously linked, explaining the example, the author writes down:

[itex]a+ \frac{1}{b(a-b)}=(a-b)+b+\frac{1}{b(a-b)}[/itex]

Now, where does that come from?

## The Attempt at a Solution

As the title says, at least I am aware of what the topic is... (!). So everything moves around the AM-GM inequality.

[itex]\frac{a_1 + \dots + a_n}{n} \geq \sqrt[n]{a_1 \dots a_n}[/itex]

I have to admit I have some troubles figuring out what's going on here, so it's not a matter of solving something, it's more about showing why I don't see the solution.

I tried to manipulate a bit the first formula, but it's not about that I guess, cause I really cannot see how the equality in

**2.**stands.

So, I am looking forward to any feedback. Thanks a lot.