Question

x+y=5 ; x^2-y^2=15
calculati: (x-y)+(x-y)^2+(x-y)^3

Answer 1

x^2-y^2=(x+y)(x-y)
15=5•(x-y)
x-y=3
(x-y)+(x+y)^2+(x-y)^3=
3+3^2+3^3=
3+9+27=
39

Answer 2

[tex]x+y=5\;\\ si\;\;x^2-y^2=15\;\\adica:\;(x+y)(x-y)=15\Leftrightarrow\;5(x-y)=15\;\Rightarrow\;\boxed{x-y=3}\\ \\ (x-y)+(x-y)^2+(x-y)^3=3+3^2+3^3=39[/tex]