Originally Posted bySuperTu

I presume you mean the minimum value of y?

Set

Find a common denominator:

Thus:

Square both sides:

=

If you expand this on both sides of the equation you will find that you are left with a quadratic (there are a number of nice cancellations) that you can solve for x. Then put this value of x into the y equation to find a value of y. (Make sure that the final value you claim is the answer is, in fact, a minimum not a maximum.)

A quicker way to do this is logical. You are adding two positive terms to find a minimum, so find the minimum values of and . Then add these to get the minimum value for y.

-Dan