Nadianad1viz
Rozwiązane

Wyznacz wielomiany f (x y) i g(x y)takie, że
3f(x,y)+g(x,y)=7x^2y-2y^4+xy
4f(x,y)-g(x,y)=14x^2y+9y^4-8xy

Odpowiedź :

Konrad509viz

[tex]3f(x,y)+g(x,y)=7x^2y-2y^4+xy\\\underline{4f(x,y)-g(x,y)=14x^2y+9y^4-8xy}\\7f(x,y)=21x^2y+7y^4-7xy\\\boxed{f(x,y)=3x^2y+y^4-xy}\\\\3(3x^2y+y^4-xy)+g(x,y)=7x^2y-2y^4+xy\\9x^2y+3y^4-3xy+g(x,y)=7x^2y-2y^4+xy\\\boxed{g(x,y)=-2x^2y-5y^4+4xy}[/tex]