Question

Решите( 1. y=x^2+5x+6 y=0 x=0 2. y=x^2-6x+8 x=0 y=0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the given equations, you need to find the values of 'x' when 'y' is equal to 0 and vice versa. Let's solve each equation one by one:

1. y = x^2 + 5x + 6, y = 0:

To find the values of 'x' when y = 0, we need to set the equation equal to zero and solve for 'x':

x^2 + 5x + 6 = 0

Now, we can factor the quadratic equation:

(x + 2)(x + 3) = 0

Now, set each factor to zero and solve for 'x':

x + 2 = 0 -> x = -2 x + 3 = 0 -> x = -3

So, the solutions for the equation are x = -2 and x = -3.

2. y = x^2 - 6x + 8, x = 0:

To find the values of 'y' when x = 0, we need to substitute x = 0 in the equation and solve for 'y':

y = (0)^2 - 6(0) + 8 y = 8

So, the solution for this case is y = 8.

Now, let's find y = 0:

x^2 - 6x + 8 = 0

This quadratic equation doesn't factor easily, so let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

For the equation x^2 - 6x + 8 = 0, a = 1, b = -6, and c = 8.

x = [6 ± √((-6)^2 - 4(1)(8))] / 2(1) x = [6 ± √(36 - 32)] / 2 x = [6 ± √4] / 2 x = [6 ± 2] / 2

Now, calculate both solutions for 'x':

1. x = (6 + 2) / 2 x = 8 / 2 x = 4

2. x = (6 - 2) / 2 x = 4 / 2 x = 2

So, the solutions for the equation y = x^2 - 6x + 8 are x = 4 and x = 2.

In summary:

1. For y = x^2 + 5x + 6, the solutions are x = -2 and x = -3.
2. For y = x^2 - 6x + 8, the solutions are x = 4 and x = 2.