Question

3(2×+1)²+10(2×+1)+3=0

Answer 1

Ответ:

Смотри решение на фото

Answer 2

To solve the equation 3(2x+1)² + 10(2x+1) + 3 = 0, you can use a substitution method. Let's set y = 2x + 1. This will simplify the equation:

3y² + 10y + 3 = 0

Now, we have a quadratic equation in terms of y. You can solve this quadratic equation using the quadratic formula:

y = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 3, b = 10, and c = 3. Plug these values into the formula:

y = (-10 ± √(10² - 4 * 3 * 3)) / (2 * 3)

Now, calculate the discriminant (the value inside the square root):

Discriminant = 10² - 4 * 3 * 3 = 100 - 36 = 64

Now, continue solving for y:

y = (-10 ± √64) / (2 * 3)

y = (-10 ± 8) / 6

Now, you have two possible solutions for y:

1. y = (-10 + 8) / 6 = -2 / 6 = -1/3
2. y = (-10 - 8) / 6 = -18 / 6 = -3

Now that you have the values for y, you can find the corresponding values for x:

For y = -1/3: 2x + 1 = -1/3

Subtract 1 from both sides: 2x = -1/3 - 1

2x = -4/3

Divide by 2: x = (-4/3) / 2

x = -2/3

For y = -3: 2x + 1 = -3

Subtract 1 from both sides: 2x = -3 - 1

2x = -4

Divide by 2: x = -4 / 2

x = -2

So, the solutions for the original equation 3(2x+1)² + 10(2x+1) + 3 = 0 are:

x = -2/3 and x = -2