Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 1330

а) $$ \left\{\begin{array}{l} 2 x^2-x y=y^2+5 \\ x^2-x y=y^2+1 \end{array}\right. $$
    x² = 4     x = ±2
    $$ \left\{\begin{array} { l } { x = 2 } \\ { 2 ^ { 2 } - 2 y = y ^ { 2 } + 1 } \end{array} \left\{\begin{array}{l} x=2 \\ -y^2-2 y+3=0 \end{array}\right.\right. $$
    $$ \begin{aligned} & y^2+2 y-3=0 \\ & y_1=1 \\ & y_2=-3 \end{aligned} \left\lvert\, \Rightarrow\left[\begin{array}{l} \left\{\begin{array}{l} x_1=2 \\ y_1=1 \end{array}\right. \\ \left\{\begin{array}{l} x_2=2 \\ y_2=-3 \end{array}\right. \end{array}\right.\right. $$
    $$ \left\{\begin{array} { l } { x = - 2 } \\ { ( - 2 ) ^ { 2 } + 2 y = y ^ { 2 } + 1 } \end{array} \left\{\begin{array}{l} x=-2 \\ -y^2+2 y+3=0 \end{array}\right.\right. $$
    $$ \begin{aligned} & y^2-2 y-3=0 \\ & y_3=-1 \\ & y_4=3 \end{aligned} \left\lvert\, \Rightarrow\left[\begin{array}{l} \left\{\begin{array}{l} x_3=-2 \\ y_3=-1 \end{array}\right. \\ \left\{\begin{array}{l} x_4=-2 \\ y_4=3 \end{array}\right. \end{array}\right.\right. $$
    (2; 1), (2; −3), (−2; −1), (−2; 3)
$$ \text { б) }\left\{\begin{array}{l} 3 x^2-2 y^2=2 x y-1 \\ 2 x^2-y^2=2 x y-1 \end{array}\right. $$
    x² − y² = 0     (x − y)(x + y) = 0
    $$ \left\{\begin{array} { l } { x - y = 0 } \\ { 2 x ^ { 2 } - y ^ { 2 } = 2 x y - 1 } \end{array} \left\{\begin{array} { l } { x = y } \\ { 2 y ^ { 2 } - y ^ { 2 } = 2 y ^ { 2 } - 1 } \end{array} \left\{\begin{array} { l } { x = y } \\ { y ^ { 2 } = 1 } \end{array} \left[\begin{array}{l} \left\{\begin{array}{l} x=1 \\ y=1 \end{array}\right. \\ \left\{\begin{array}{l} x=-1 \\ y=-1 \end{array}\right. \end{array}\right.\right.\right.\right. $$
    $$ \left\{\begin{array} { l } { x + y = 0 } \\ { 2 x ^ { 2 } - y ^ { 2 } = 2 x y - 1 } \end{array} \left\{\begin{array} { l } { x = - y } \\ { 2 y ^ { 2 } - y ^ { 2 } = - 2 y ^ { 2 } } \end{array} \left\{\begin{array}{l} x=-y \\ 3 y^2=-1 \end{array}\right.\right.\right. $$     нет корней
    (1; 1), (−1; −1)