Question

Решите систему уравнений пожалуйста
x^2/y+y^2/x=18
{
х+у=12

Answer 1

$left { {{ frac{ x^{2} }{y}+ frac{ y^{2} }{x}=18 } atop {x+y=12}} right.\\left { {{ frac{ x^{3}+ y^{3} }{yx}=18 } atop {x=12-y}} right.\\left { {{ frac{(x+y)( x^{2} -xy+ y^{2}) }{yx} } atop {x=12-y}} right.\\left { {{ frac{12((12-y)^{2}-y(12-y)+y^{2}) }{y(12-y)}=18 } atop {x=12-y}} right.\\left { {{ frac{2(144-24y+y^{2}-12y+2y^{2}) }{y(12-y)} }=3 atop {x=12-y}} right.\\left { {{ frac{2y^{2}-24y+96}{y(12-y)}=1 } atop {x=12-y}} right.$
$2y^{2}-24y+96=12y-y^{2} \ y^{2}-12y+32=0 \ D=b^{2}-4ac = 144-128=16 \ y_{1}= frac{-b+ sqrt{D} }{2a}= frac{12-4}{2}=4 \ y_{2}= frac{-b- sqrt{D} x}{2a}= frac{12+4}{2}=8 \ x_{1}=12- y_{1}=8 \ x_{2}=12- y_{2}=4$

Ответ: {8; 4}, [4; 8}