# Explain Please?

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if #x+y=4# for positive integers

x and y , then the smallest possible value of #1/x + 1/y #

if

x and y , then the smallest possible value of

##### 3 Answers

1

#### Explanation:

There are only two possible combinations of positive integer

Let

Let

Therefore, since

Isn't it 1

#### Explanation:

Substituting in the equation:

LCM of denominators is

Combining the denominators:

Given:

Minimize:

Substitute

Compute the first derivative with respect to x:

To find local extrema we set the first derivative equal to 0:

Multiply both sides by

Expand the square:

Find the corresponding value of y:

The value is:

We could perform the second derivative test but we know that this is a minimum because it is obvious that the maximum occurs when either