Verified answer

Ответ:

1)

[tex]\displaystyle \left \{ {{ x = -6 } \atop { y = -7 }} \right.[/tex]

2)

[tex]\left [ \begin{array}{l} \displaystyle \left \{ {{ x = 3 } \atop { y = -\dfrac{2}{3} }} \right \\ \\\displaystyle \left \{ {{ x = -3 } \atop { y = \dfrac{2}{3} }} \right. \end{array} \right[/tex]

3)

[tex]\left [ \begin{array}{l} \displaystyle \left \{ {{ x = 2 } \atop { y = 1}} \right \\ \\\displaystyle \left \{ {{ x = -1,8 } \atop { y = 0,24 }} \right. \end{array} \right[/tex]

Примечание:

Комплексным числом называют число вида:

[tex]z = a +bi[/tex], где [tex]a,b \in \mathbb R[/tex], а число [tex]i[/tex] - называется мнимой единицей и для которой верное тождество [tex]i^{2} = -1[/tex]

Два комплексных числа [tex]z_{1} = a_{1} + b_{1}i[/tex] и [tex]z_{2} = a_{2} + b_{2}i[/tex] называют равными [tex](z_{1} = z_{2})[/tex] если:

[tex]\displaystyle[/tex][tex]\displaystyle \left \{ {{a_{1} = a_{2}} \atop {b_{1}=b_{2}}} \right.[/tex]

Разность квадратов:

[tex]\boxed{a^{2} - b^{2} = (a - b)(a + b)}[/tex]

Пошаговое объяснение:

20.4

1) [tex]x + (x - y )i = -6 + i[/tex]

[tex]\displaystyle \left \{ {{x = -6} \atop {x - y = 1}} \right.[/tex]

[tex]-6 - y =1[/tex]

[tex]y = -6 - 1 = -7[/tex]

2) [tex]x^{2} + xyi = 9 - 2i[/tex]

[tex]\displaystyle \left \{ {{x^{2} = 9} \atop {xy =-2}} \right.[/tex] [tex]\displaystyle \left \{ {{x^{2} = 9} \atop {y =- \dfrac{2}{x} }} \right.[/tex]

[tex]x^{2} = 9[/tex]

[tex]x^{2} =3^{2}[/tex]

[tex]x^{2} - 3^{2} = 0[/tex]

[tex](x - 3)(x + 3) = 0 \Longrightarrow x_{1,2} = \pm 3[/tex]

[tex]y_{1} = - \dfrac{2}{x_{1}} = -\dfrac{2}{3}[/tex]

[tex]y_{1} = - \dfrac{2}{x_{2}} = -\dfrac{2}{-3} = \dfrac{2}{3}[/tex]

3) [tex](x^{2} + 5yi) -(y + xi) = 3 + 3i[/tex]

[tex]x^{2} + 5yi - y - xi = 3 + 3i[/tex]

[tex]x^{2} - y + 5yi - xi = 3 + 3i[/tex]

[tex]x^{2} - y + (5y - x)i = 3 + 3i[/tex]

[tex]\displaystyle \left \{ {{x^{2} - y = 3} \atop {5y - x = 3}} \right. \left \{ {{y = x^{2} -3} \atop {5y - x = 3}} \right \Longrightarrow 5(x^{2} - 3) - x = 3[/tex]

[tex]5(x^{2} - 3) - x = 3[/tex]

[tex]5x^{2} - 15 - x = 3[/tex]

[tex]5x^{2} - x - 18 = 0[/tex]

[tex]D = 1 - 4 \cdot 5 \cdot (-18) = 1 + 360 = 361 = 19^{2}[/tex]

[tex]x_{1} = \dfrac{1 + 19}{2 \cdot 5} = \dfrac{20}{10} = 2[/tex]

[tex]x_{2} = \dfrac{1 - 19}{2 \cdot 5} = \dfrac{-18}{10} = -1,8[/tex]

[tex]y_{1} = x_{1}^{2} - 3 = 2^{2} - 3 = 4- 3 = 1[/tex]

[tex]y_{2} = x_{2}^{2} - 3 = 3,24 - 3 = 0,24[/tex]