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Consider the polynomial p(x,y)=x4+y4+x2+y2. Express p(x,y) as the sum of squares of three polynomials over R in x and y .
Let real constant t=sqrt{sqrt{8}-2}
so that frac{t^{4}}{4}+t^{2}=1
then (-x^{2}+frac{t^{2}}{2}y^{2})^{2}+(ty^{2}+x)^{2}+(txy-y)^{2}=x^{4}+y^{4}+x^{2}+y^{2}.
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