Question

(x*3 + y*3 = 2,
xy(x + y) = 2;​

Answer 1

$\left\{\begin{array}{l}x^3+y^3=2\\xy(x+y)=2\end{array}\right\ \ \left\{\begin{array}{l}x^3+y^3=2\\x^2y+xy^2=2\ |\cdot 3\end{array}\right\ \oplus \ \left\{\begin{array}{l}x^2+3x^2y+3xy^2+y^3=8\\x^2y+xy^2=2\end{array}\right$

$\left\{\begin{array}{l}(x+y)^3=8\\xy(x+y)=2\end{array}\right\ \ \left\{\begin{array}{l}x+y=2\\xy\cdot 2=2\end{array}\right\ \ \left\{\begin{array}{l}x+y=2\\xy=1\end{array}\right\ \ \left\{\begin{array}{l}y=2-x\\x(2-x)=1\end{array}\right$

$\left\{\begin{array}{l}y=2-x\\2x-x^2=1\end{array}\right\ \ \left\{\begin{array}{l}y=2-x\\x^2-2x+1=0\end{array}\right\ \ \left\{\begin{array}{l}y=2-x\\(x-1)^2=0\end{array}\right\ \ \left\{\begin{array}{l}y=2-1=1\\x=1\end{array}\right\\\\\\Otvet:\ \ (\, 1\, ;\, 1\, )\ .$