Question

3.Решите систему уравнений:
х=у²-4у,
х+у=4.
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Answer 1

Ответ и объяснение:

x = y^2 - 4y;

x + y = 4;

x = 4 - y;

4 - y = y^2 - 4y;

y^2 - 3y - 4 = 0;

D = 9 + 16 = 25;

y1 = (3 - 5)/2 = -2/2 = -1

y2 = (3 + 5)/2 = 8/2 = 4

x1 = 4 - y1 = 4 + 1 = 5

x2 = 4 - y2 = 4 - 4 = 0

Answer 2

Объяснение:

$\left\{\begin{array}{ccc}x=y^2-4y\\x+y=4\\\end{array}\right \ \ \ \ \left\{\begin{array}{ccc}4-y=y^2-4y\\x=4-y\\\end{array}\right \ \ \ \ \left\{\begin{array}{ccc}y^2-3y-4=0\\x=4-y\\\end{array}\right\\\\\left\{\begin{array}{ccc}D=25\ \ \ \ \sqrt{D}=5 \\x=4-y\\\end{array}\right\ \ \ \ \left\{\begin{array}{ccc}y_1=-1\ \ \ \ y_2=4\\x_1=5\ \ \ \ x_2=0\\\end{array}\right ..$

Ответ:  (5;-1),    (0;4).