How to solve the following pair of non-linear equations $x^3+y^3=152\\x^2y+xy^2=120$
Best regards !

Another method :
Suppose $x,y$ be the roots of  $z^2+az+b=0$
$x+y=-a$ and $xy=b$
$x^3+y^3=(x+y)^3-3xy(x+y)=-a^3+3ab=152$
$xy(x+y)=-ab=120$
$a^3=-152-3*120=-512$
$a=-8$  and  $b=120/8=15$
Solve of  $z^2-8z+15=0$  for $x$ and $y$
