a)10x^2 + 5x - 5 = 0D = 5^2 - 410(-5) = 25 + 200 = 225x1 = (-5 + √225) / (210) = (-5 + 15) / 20 = 10 / 20 = 1/2x2 = (-5 - √225) / (210) = (-5 - 15) / 20 = -20 / 20 = -1
Ответ: x1 = 1/2, x2 = -1
б)x^2 - 2x - 4 = 0D = (-2)^2 - 41(-4) = 4 + 16 = 20x1 = (2 + √20) / 2 = (2 + 2√5) / 2 = 1 + √5x2 = (2 - √20) / 2 = (2 - 2√5) / 2 = 1 - √5
Ответ: x1 = 1 + √5, x2 = 1 - √5
в)-2x^2 + 12x - 18 = 0Делим все коэффициенты на -2:x^2 - 6x + 9 = 0(x - 3)^2 = 0x - 3 = 0x = 3
Ответ: x = 3
г)12x^2 - 12 = 0Делим все коэффициенты на 12:x^2 - 1 = 0(x - 1)(x + 1) = 0x - 1 = 0 or x + 1 = 0x = 1 or x = -1
Ответ: x = 1 или x = -1
a)
10x^2 + 5x - 5 = 0
D = 5^2 - 410(-5) = 25 + 200 = 225
x1 = (-5 + √225) / (210) = (-5 + 15) / 20 = 10 / 20 = 1/2
x2 = (-5 - √225) / (210) = (-5 - 15) / 20 = -20 / 20 = -1
Ответ: x1 = 1/2, x2 = -1
б)
x^2 - 2x - 4 = 0
D = (-2)^2 - 41(-4) = 4 + 16 = 20
x1 = (2 + √20) / 2 = (2 + 2√5) / 2 = 1 + √5
x2 = (2 - √20) / 2 = (2 - 2√5) / 2 = 1 - √5
Ответ: x1 = 1 + √5, x2 = 1 - √5
в)
-2x^2 + 12x - 18 = 0
Делим все коэффициенты на -2:
x^2 - 6x + 9 = 0
(x - 3)^2 = 0
x - 3 = 0
x = 3
Ответ: x = 3
г)
12x^2 - 12 = 0
Делим все коэффициенты на 12:
x^2 - 1 = 0
(x - 1)(x + 1) = 0
x - 1 = 0 or x + 1 = 0
x = 1 or x = -1
Ответ: x = 1 или x = -1