Question

Решите систему уравнений :

x+y=20
x^2+y^2=20

Answer 1

$left { {{x+y=20} atop {x^2+y^2=20}} right.; left { {{(x+y)^2=400} atop {x^2+y^2=20}} right. ; left { {{(x^2+y^2)+2xy=400} atop {x^2+y^2=20}} right. ; left { {{20+2xy=400} atop {x^2+y^2=20}} right. \\ left { {{2xy=380} atop {x^2+y^2=20}} right. ; left { {{xy=190} atop {x^2+y^2=20}} right. ; left { {{y=frac{190}{x}} atop {x^2+y^2=20}} right. \\x^2+frac{190^2}{x^2}=20; |cdot x^2; (xne 0)\\x^4+190^2=20x^2\\t=x^2; ; Rightarrow quad t^2-20t+36100=0$

$D=400-4cdot 36100 textless 0; ; ; Rightarrow quad net; ; dejstvit.; ; reshenij$

Система не имеет решений