Question

Решите систему уравнений:
$\left \{ {{x^2y+xy^2=126} \atop {x+y=9}} \right.$

Answer 1

$\left \{ {{x^2y+xy^2=126} \atop {x+y=9}} \right. \\ \left \{ {{xy(x+y)=126} \atop {x+y=9}} \right. \\ xy*9=126\\ xy=14\\ \left \{ {{xy=14} \atop {x=9-y}} \right. \\ (9-y)y=14\\ 9y-y^2=14\\ y^2-9y+14=0\\ D=81-4*1*14=25\\ y_1= \frac{9+5}{2}=7\\ y_2= \frac{9-5}{2}=2\\ x_1=9-7=2\\ x_2=9-2=7$