Monday Math 67

Suppose that x, y, and z are positive real numbers with x+y+z=1. Then find (without calculus) the minimum value of .

Here, we can use the AM-GM inequality:

and
,
but , so
,
and so


and so , with equality when .

Advertisements

Tags: , , , , ,

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


%d bloggers like this: