Question

3+20b-7b^2=0 7b^2-6b-1=0 решить уравнения

Answer 1

Решение в прикреплённом изображении

Answer 2

To solve the quadratic equation 7b^2 - 6b - 1 = 0, we can use the quadratic formula:

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 7, b = -6, and c = -1.

Plugging these values into the formula:

b = [6 ± √((-6)^2 - 4 * 7 * (-1))] / 2 * 7 b = [6 ± √(36 + 28)] / 14 b = [6 ± √64] / 14 b = [6 ± 8] / 14

Now, we have two possible solutions:

1. When b = (6 + 8) / 14 = 14 / 14 = 1.
2. When b = (6 - 8) / 14 = -2 / 14 = -1/7.

So, the solutions to the quadratic equation are b = 1 and b = -1/7.

Now, let's check these solutions by substituting them back into the original equation 3 + 20b - 7b^2 = 0:

1. For b = 1: 3 + 20(1) - 7(1)^2 = 3 + 20 - 7 = 16, which is not equal to 0, so b = 1 is not a solution.

2. For b = -1/7: 3 + 20(-1/7) - 7(-1/7)^2 = 3 - 20/7 - 7(1/49) = 3 - 20/7 - 1/7 = (3 * 7 - 21)/7 = 0, which is equal to 0, so b = -1/7 is a solution.

Thus, the only valid solution for the original equation is b = -1/7.