Question

пусть ху=q , x+y=p найдите x^4+y^4

Answer 1

x^4+y^4=(x^2+y^2)^2-2x^2y^2=((x+y)^2-2xy)^2-2(xy)^2=

=(p^2-2q)^2-2q^2=p^4-4p^2q+4q^2-2q^2=p^4-4p^2q+2q^2

ответ:p^4-4p^2q+2q^2