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Saurav
 
 

DS: Is x^4 + y^4 > z^4 ?

by Saurav Sat Oct 18, 2008 1:43 pm

Is x^4 + y^4 > z^4 ?

1. x^2 + y^2 > z^2

2. x + y > z
divya
 
 

by divya Mon Oct 20, 2008 3:37 pm

RonPurewal
Students
 
Posts: 19744
Joined: Tue Aug 14, 2007 8:23 am
 

by RonPurewal Fri Nov 07, 2008 4:59 am

heh heh, that problem.

let me say the following:

this problem should serve as a nice wake-up call to any and all students who don't like "plug-in methods", or who abjure such methods so that they can keep searching ... and searching ... and searching for the elusive "textbook" method.
this problem is pretty much ONLY soluble with plug-in methods. therefore, you MUST make plug-in methods part of your arsenal if you want a fighting chance at all quant problems you'll see.

this is the case for a great many difficult inequality problems, by the way: the most difficult among those problems will often require some sort of plug-ins, or, at the very least, they will be hell on earth if you try to use theory.