Question

Решите систему:
x^2/y+y^2/x=18
x+y=12

/ - знак дроби

Answer 1

{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)