Question

39. 1)х^2 - 3x - 12 = 6; 2) х^2 - 9x - 4 = 1;3)x^2 + 8x = 16 - 2x;4) x^2 + x - 3= 1 - 5x.​

Answer 1

Ответ:

1)64

2)38

3)29

4)26

Вот так вот

Answer 2

Let's solve each of the given quadratic equations:

1. x^2 - 3x - 12 = 6

To solve this equation, we can rearrange it into standard quadratic form:

x^2 - 3x - 18 = 0

Now we can factorize it:

(x - 6)(x + 3) = 0

Setting each factor equal to zero, we get:

x - 6 = 0 --> x = 6 x + 3 = 0 --> x = -3

So the solutions to the equation are x = 6 and x = -3.

2. x^2 - 9x - 4 = 1

Rearranging the equation:

x^2 - 9x - 5 = 0

This quadratic equation does not factorize easily. We can solve it by using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -9, and c = -5. Substituting these values into the formula:

x = (-(-9) ± sqrt((-9)^2 - 4(1)(-5))) / 2(1) = (9 ± sqrt(81 + 20)) / 2 = (9 ± sqrt(101)) / 2

So the solutions to the equation are x = (9 + sqrt(101))/2 and x = (9 - sqrt(101))/2.

3. x^2 + 8x = 16 - 2x

Rearranging the equation:

x^2 + 10x - 16 = 0

Again, this quadratic equation does not factorize easily. We can use the quadratic formula to solve it:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = 10, and c = -16. Substituting these values into the formula:

x = (-(10) ± sqrt((10)^2 - 4(1)(-16))) / 2(1) = (-10 ± sqrt(100 + 64)) / 2 = (-10 ± sqrt(164)) / 2

So the solutions to the equation are x = (-10 + sqrt(164))/2 and x = (-10 - sqrt(164))/2.

4. x^2 + x - 3 = 1 - 5x

Rearranging the equation:

x^2 + x + 5x - 3 - 1 = 0

Simplifying:

x^2 + 6x - 4 = 0

This quadratic equation does not factorize easily. We can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 6, and c = -4. Substituting these values into the formula:

x = (-(6) ± sqrt((6)^2 - 4(1)(-4))) / 2(1) = (-6 ± sqrt(36 + 16)) / 2 = (-6 ± sqrt(52)) / 2 = (-6 ± 2sqrt(13)) / 2 = -3 ± sqrt(13)

So the solutions to the equation are x = -3 + sqrt(13) and x = -3 - sqrt(13).