[tex]\displaystyle Sistemul~este~echivalent~cu \left \{ {{(x-y)^2(x+y)=3} \atop {(x+y)(x^2+y^2)=15}} \right. . \\ \\ Notand~s=x+y~si~p=xy,~acesta~se~rescrie \\ \\ \left \{ {{(s^2-4p)s=3} \atop {s(s^2-2p)}=15} \right. \Leftrightarrow \left \{ {{s^3-4ps=3~~~~~~(a)} \atop {s^3-2ps=15}~~~~~(b)} \right. . \\ \\ 2(b)-(a) \Rightarrow s^3=27 \Rightarrow s=3.~Rezulta~p=2. \\ \\ Deci~avem~ \left \{ {{x+y=3} \atop {xy=2}} \right.,~si,~deci,~solutiile~sistemului~sunt \\ \\ (1,2)~si~(2,1).[/tex]
