Question

15х2+2х-8=0В Ответ записать значение выражения 3х1-5х2

Answer 1

$15 {x}^{2} + 2x - 8 = 0 \\ D = {2}^{2} - 4 \times 15 \times ( -8 ) = \\ = 4 + 320 = 324 = {18}^{2} \\ x_½ = \frac{ - 2±18}{2 \times 15} \\ x_1 = - \frac{2}{3} \: \: \: \: \: x_2 = \frac{8}{15} \\ \\ 3 \times x_1 - 5 \times x_2 = \\ = 3 \times ( - \frac{2}{3} ) - 5 \times \frac{8}{15} = \\ = - 2 - \frac{8}{3} = - 4 \frac{2}{3}$

Answer 2

To find the value of the expression 3x1 - 5x2, we first need to solve the equation 15x2 + 2x - 8 = 0.

To solve the equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 15, b = 2, and c = -8. Plugging these values into the quadratic formula, we have:

x = (-2 ± √(2^2 - 4 * 15 * -8)) / (2 * 15) = (-2 ± √(4 + 480)) / 30 = (-2 ± √484) / 30 = (-2 ± 22) / 30

Now, we have two possible solutions:

1. When x = (-2 + 22) / 30 = 20 / 30 = 2/3
2. When x = (-2 - 22) / 30 = -24 / 30 = -4/5

Now, we can substitute these values into the expression 3x1 - 5x2:

1. When x = 2/3: 3(2/3) - 5x2 = 6/3 - 5x2 = 2 - 5x2

2. When x = -4/5: 3(-4/5) - 5x2 = -12/5 - 5x2

So, depending on the value of x, the expression 3x1 - 5x2 can be either 2 - 5x2 or -12/5 - 5x2.