Question

Решите срочно пожалуйста!!!!!!!!!!!!!!​

Answer 1

Ответ:

$1)\ \ \left\{\begin{array}{l}x^2+y^2+2(x-y)+2=0\\z^2+xz+yz-4=0\end{array}\right\\\\\\a)\ \ x^2+y^2+2x-2y+1+1=0\\\\(x^2+2x+1)+(y^2-2y+1)=0\\\\(x+1)^2+(y-1)^2=0\ \ \Rightarrow \ \ \ \left\{\begin{array}{l}x+1=0\\y-1=0\end{array}\right\ \ \left\{\begin{array}{l}x=-1\\y=1\end{array}\right\\\\b)\ \ z^2+xz+yz-4=z^2-1\cdot z+1\cdot z-4=z^2-4\ \ ,\ \ z^2-4=0\ \ ,\\\\(z-2)(z+2)=0\ \ ,\ \ z_1=-2\ ,\ z_2=2\\\\Otvet:\ \ (-1;1;-2)\ ,\ (-1;1;2)\ .$

$2)\ \ \left\{\begin{array}{l}x^2+y^2+z^2=xy+yz+zx\\2x+3y-6z-1=0\end{array}\right\\\\a)\ \ x^2+y^2+z^2=xy+yz+zx\ |\cdot 2\\\\2x^2+2y^2+2z^2-2xy-2yz-2zx=0\\\\x^2+y^2+z^2-2xy-2yz-2zx+x^2+y^2+z^2=0\\\\(x^2-2xy+y^2)+(y^2-2yz+z^2)+(z^2-2zx+x^2)=0\\\\(x-y)^2+(y-z)^2+(z-x)^2=0\ \ \Rightarrow \ \ \left\{\begin{array}{l}x-y=0\\y-z=0\\z-x=0\end{array}\right\ \ \left\{\begin{array}{l}x=y\\y=z\\z=x\end{array}\right\ \Rightarrow \\\\x=y=z$

$b)\ \ \left\{\begin{array}{l}x=y=z\\2x+3y-6z-1=0\end{array}\right\ \ \left\{\begin{array}{l}x=y=z\\2x+3x-6x-1=0\end{array}\right\\\\\\\left\{\begin{array}{l}x=y=z\\-x-1=0\end{array}\right\ \ \left\{\begin{array}{l}x=y=z\\x=-1\end{array}\right\ \ \ \ \Rightarrow \ \ \ \ x=y=z=-1\\\\\\Otvet:\ \ (-1\, ;-1\, ;-1\, )\ .$