Б) x^2 - y = 2
X + y = 4
x^2 - (4-x) = 2
y = 4 -x
x^2 + x - 6 = 0
y = 4-x
D = 1 + 24 = 5^2
X1 = (-1 + 5)/2 = 2
X2 = (-1-5)/2 = -3
Y1 = 4-2 = 2
Y2 = 4-(-3) = 7
в) x^2 + y^2 = 25
xy = 12
x^2 + (12/x)^2 = 25
y = 12/x
X^2 + 144/x^2 = 25|*x^2
Y = 12/x
X^4 - 25x^2 + 144 = 0
Y = 12/x
Пусть x^2 = t, t>=0
T^2 - 25t +144 = 0
D = 625 - 576 = 49 = 7^2
T1 = (25+7)/2 = 16
T2 = (25-7)/2 = 9
X^2 = 16
X1 = 4
Y1 = 12/4 = 3
X2 = -4
Y2 = 12/-4 = -3
X^2 = 9
X1 = 3
Y1 = 12/3 = 4
X2 = -3
Y2 = 12/-3 = -4
б) y - 5x = 3
- x^2 - 2xy + y^2 = -1
Y = 3+5x
-x^2 -2x(3+5x) + (3+5x)^2 = -1
Y = 3+5x
-x^2 - 6x - 10x^2 + 9 + 30x + 25x^2 = -1
Y = 3+5x
14x^2 + 24x + 10 = 0
Y = 3+5x
7x^2 + 12x + 5 = 0
D = 144 - 140 = 2^2
X1 = (-12+2)/14 = -5/7
X2 = (-12-2)/14 = -1
Y1 = 3 + 5*(-5/7) = 3 - 25/7 = 4/7
Y2 = 3 + 5*(-1) = -2
в)x^2 + y^2 + 2xy = 49
X - y = 3
(3 + y)^2 + y^2 + 2y(3 + y) = 49
X = 3 + y
9 + 6y + y^2 + y^2 + 6y + 2y^2 = 49
X = 3+y
4y^2 + 12y - 40 = 0
X = 3+y
Y^2 + 3y - 10 = 0
X= 3+y
D= 9 + 40 = 7^2
Y1 = (-3+7)/2 = 2
Y2 = (-3-7)/2 = -5
X1 = 3+2 = 5
X2 = 3 -5 = -2