Question

若x^4+y^4=15,xy^2-x^2y=-5,求x^4-y^4+3xy^2-x^2y-2xy^2+2y^4

Answer 1

x^4-y^4+ 3xy^2-x^2y-2xy^2+2y^4

= (x^2)^2-(y^2)^2+xy(3y-x-2y)+2(y^2)^2

=(x^2)^2+(y^2)^2+xy(y-x)

=10