Minimization Rule to find step-size in a Quadratic Programming Problem

Hi MHF. Clearly my first post here, so first of all let me say hello ((Hi)) and quickly apologise if this post is in the wrong forum. I am happy to remove the remove the post and re-post it if it is necessary.

I've been really struggling on the following problem for the past few days, so any help at all or a push in the right direction would be frankly a dream.

http://i.imgur.com/hVvffso.png?1

I've been able to make a start on it, but have literally no idea how to proceed.

Please have a look at my workings so far, I've labelled the lines so you can hopefully reference them easier:

http://i.imgur.com/bAbJGmQ.png

Sorry, I'm not very apt at using LaTeX online.

Am I going about this the right way? Or should I even be trying something else to find the step-size tau? I thought about proving it by induction, but couldn't see any way I could get the desired result really.

Again, any help at all on this would be really, really appreciated. Thanks so much in advance! x (Nod)