Question

Решите уравнения: 1. (x-2)(x-3)= 0 2. x в квадрате -4х=0 3. х в квадрате -9х+14=0

Answer 1

Раскроем выражение в уравнении
(x - 3)*(x - 2)
Получаем квадратное уравнение
 6 + x² - 5*x = 0
Это уравнение вида
a*x^2 + b*x + c.
Квадратное уравнение можно решить с помощью дискриминанта.Корни квадратного уравнения:
                         ___
              - b ± \/ D
 x1, x2 = -----------,
                 2*a
где D = b^2 - 4*a*c - это дискриминант.
Т.к.a = 1
b = -5
c = 6,
тоD = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (6) = 1
Т.к. D > 0, то уравнение имеет два корня.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
x1 = 3
x2 = 2




-4*x = 0
Разделим обе части ур-ния на -4
x = 0 / (-4)
Получим ответ: x = 0


-9*x+14 = 0
Переносим свободные слагаемые (без x)из левой части в правую, получим:
-9*x = -14
Разделим обе части ур-ния на -9
x = -14 / (-9)
Получим ответ: x = 14/9

Answer 2

1. (x-2)(x-3) = 0

To solve this equation, we set each factor equal to zero and solve for x:

x - 2 = 0 or x - 3 = 0

Solving the first equation: x - 2 = 0 x = 2

Solving the second equation: x - 3 = 0 x = 3

Therefore, the solutions to the equation (x-2)(x-3) = 0 are x = 2 and x = 3.

2. x^2 - 4x = 0

To solve this equation, we factor out the common factor x:

x(x - 4) = 0

Now we set each factor equal to zero and solve for x:

x = 0 or x - 4 = 0

Solving the second equation: x - 4 = 0 x = 4

Therefore, the solutions to the equation x^2 - 4x = 0 are x = 0 and x = 4.

3. x^2 - 9x + 14 = 0

To solve this equation, we can either factor it or use the quadratic formula. Let's try factoring:

(x - 7)(x - 2) = 0

Setting each factor equal to zero and solving for x:

x - 7 = 0 or x - 2 = 0

Solving the first equation: x - 7 = 0 x = 7

Solving the second equation: x - 2 = 0 x = 2

Therefore, the solutions to the equation x^2 - 9x + 14 = 0 are x = 7 and x = 2.