1. x² - 6x + 9 = 0
D = 0
x = -b/2a = 6/2 = 3
Відповідь: в) 1
2. x² - 7x = -6
x² - 7x + 6 = 0
D = b² - 4ac = 49 - 24 = 25
√D = √25 = 5
x₁ = (-b + √D)/2a = (7 + 5)/2 = 12/2 = 6
x₂ = (-b - √D)/2a = (7 - 5)/2 = 2/2 = 1
x₁ + x₂ = 6 + 1 = 7
Відповідь: а) 7
3. x² - 7x + 6 = 0
x² - 7x + 6 = 0
D = b² - 4ac = 49 - 24 = 25
√D = √25 = 5
x₁ = (-b + √D)/2a = (7 + 5)/2 = 12/2 = 6
x₂ = (-b - √D)/2a = (7 - 5)/2 = 2/2 = 1
x₁ · x₂ = 6 · 1 = 6
Відповідь: г) 6
4. x² - 15x + 56 = 0
x² - 7x - 8x + 56 = 0
x(x - 7) - 8(x - 7) = 0
(x - 7)(x - 8) = 0
x - 7 = 0
x₁ = 7
x - 8 = 0
x₂ = 8
Відповідь: в) 7i 8
1) x+2-y=2; x+3y=4; x+2>0; y>0
x=y, 4y=4; y=1; x=1; (1;1)
2) x+2-y=2; x-3y=4; x+2>0, y<0
x=y, -2y=4; y=-2; x=-2;
3) -x-2-y=2; x+3y=4; x+2<0, y>0
x=-y-4; 2y=8; y=4; x=-4-4=-8;
4) -x-2-y=2; x-3y=4; x+2<0, y<0;
x=-y-4; -4y=8; y=-2; x=2-4=-2; - не подх;
ответ: (1;1), (-2;-2) и (-8;4)