(Don't worry, this isn't the same question as I posted the other day)

Find the maximum value of

subject to the constraint

[NB: your answer should be given as a surd, not a decimal.]

To begin with, I multiplied out the function to get

Is that right? If not, can you tell me why? If it is, I then got the following partials...

...but then rearranging for , , , and put them into I get a really awful expression for and consequently awful expressions for , and (not 'cause I get that equal to )

Can anyone maybe see where I've gone wrong? I can tell you what I got for et cetera if needs be.