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## Homework Statement

Let p(x,y) be a positive polynomial of degree n ,p(x,y)=0 only at the origin.Is it possible that

the quotient p(x,y)/[absolute value(x)+absval(y)]^n will have a positive lower bound in the punctured rectangle [-1,1]x[-1,1]-{(0,0)}?

## Homework Equations

## The Attempt at a Solution

I observed that p(x,y) must have even degree.Also if the quotient tend to infinity at the origin the answer is yes.Otherwise p(x,y) must be hogeneous,and this may imly that the quotient has a positive lower bound.I need help for progressing