Решите систему:

x^2/y+y^2/x=18

x+y=12

/ - знак дроби

{x+y=12⇒y=12-x

{x²/y+y²/x=18⇒x³+y³=18xy⇒ (x+y) (x²-xy+y²) = 18⇒12 (x²-xy+y²) = 18xy

2 (x²-xy+y²) = 3xy

2 (x²-x (12-x) + (12-x) ²) = 3x (12-x)

2 (x²-12x+x²+144-24x+x²) = 3x (12-x)

6x²-72x+288-36x+3x²=0

9x²-108x+288=0

x²-12x+32=0

x1+x2=12 U x1*x2=32

x1=4⇒y1=8

x2=8⇒y2=4

(4; 8) ; (8; 4)