$x^6+y^6-(x^2+y^2)(x^4+x^2y^2)=0$
$(x^6+y^6)-x^2(x^2+y^2)^2=0$
$(x^2+y^2)^3-3x^2y^2(x^2+y^2)-x^2(x^2+y^2)^2=0$
$(x^2+y^2)(y^4-2x^2y^2)=0$
$(x^2+y^2)(2x^2-y^2)=0$ (นำ $-y^2$ หาร)
$2x^4-y^4+x^2y^2=0$
$\frac{2x^4}{y^4}-1+\frac{x^2}{y^2}=0$ (นำ $y^4$ หาร)
ให้ $\frac{x^2}{y^2}=A\ \ (A\geqslant 0)$
$2A^2+A-1=0$
$(2A-1)(A+1)=0$
$A=\frac{1}{2}$
${(\frac{x}{y})}^4=A^2=\frac{1}{4}$