Необходимо решить СЛОЖНУЮ систему из двух алгебраических уравнений:
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| x^4+x^2*y^2+y^4=133
{
| x^2-xy+y^2=7

Можно так
$left { {{x^4+x^2y^2+y^4=133} atop {x^2-xy+y^2=7}} right. Rightarrow left { {{(x^4+2x^2y^2+y^4)-x^2y^2=133} atop {x^2+y^2-xy=7}} right. Rightarrow$
$Rightarrowleft { {{(x^2+y^2)^2-x^2y^2=133} atop {x^2+y^2-xy=7}} right.$
Введем обозначения $x^2+y^2=m;xy=n.$
$left { {{m^2-n^2=133} atop m-n=7}} right. Rightarrowleft { {{(m-n)(m+n)=133} atop m-n=7}} right. Rightarrow{ {{7(m+n)=133} atop m-n=7}} right. Rightarrow{ {{m+n=19} atop m-n=7}} right. Rightarrow$
$Rightarrow{ {{m=13} atop n=6}} right.$
$left { {{x^2+y^2=13;} atop {xy=6 }} right. Rightarrowleft { {{x^2+y^2=13;} atop {2xy=12 }} right. Rightarrow { {{x^2+2xy+y^2=25;} atop {xy=6 }} right. Rightarrow{ {{(x+y)^2=25;} atop {xy=6 }} right. Rightarrow$
$left { {{ left { {{x+y=5} atop {xy=6}} right. } atop { left { {{x+y=-5} atop {xy=6}} right. }} right. Rightarrow left { {{ left { {{x=2;y=3;} atop {x=3;y=2;}} right. } atop { left { {{x=-2;y=-3;} atop {x=-3;y=-2;}} right. }} right.$