Question

1) 4x²-3x-1=02) 6x² + 7х-5=03) 18x²-9x-5=0​

Answer 1

Ответ:

1) Уравнение 4x² - 3x - 1 = 0:

Используя квадратное уравнение: x = (-b ± √(b² - 4ac)) / (2a)

a = 4, b = -3, c = -1

x = (-(-3) ± √((-3)² - 4 * 4 * (-1))) / (2 * 4)

x = (3 ± √(9 + 16)) / 8

x = (3 ± √25) / 8

x = (3 ± 5) / 8

Итак, решения:

x₁ = (3 + 5) / 8 = 8/8 = 1

x₂ = (3 - 5) / 8 = -2/8 = -1/4

2) Уравнение 6x² + 7x - 5 = 0:

a = 6, b = 7, c = -5

Используя квадратное уравнение:

x = (-7 ± √(7² - 4 * 6 * (-5))) / (2 * 6)

x = (-7 ± √(49 + 120)) / 12

x = (-7 ± √169) / 12

x = (-7 ± 13) / 12

Решения:

x₁ = (-7 + 13) / 12 = 6/12 = 1/2

x₂ = (-7 - 13) / 12 = -20/12 = -5/3

3) Уравнение 18x² - 9x - 5 = 0:

a = 18, b = -9, c = -5

Используя квадратное уравнение:

x = (-(-9) ± √((-9)² - 4 * 18 * (-5))) / (2 * 18)

x = (9 ± √(81 + 360)) / 36

x = (9 ± √441) / 36

x = (9 ± 21) / 36

Решения:

x₁ = (9 + 21) / 36 = 30/36 = 5/6

x₂ = (9 - 21) / 36 = -12/36 = -1/3

Модно лучший ответ пожалуйста! :)

Answer 2

To solve quadratic equations like the ones you've provided, you can use the quadratic formula:

For a quadratic equation in the form of ax² + bx + c = 0, the quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Let's use this formula to solve each of the equations:

1. 4x² - 3x - 1 = 0

a = 4, b = -3, c = -1

x = (-(-3) ± √((-3)² - 4 * 4 * (-1))) / (2 * 4)

x = (3 ± √(9 + 16)) / 8

x = (3 ± √25) / 8

x = (3 ± 5) / 8

So, we have two solutions:

x₁ = (3 + 5) / 8 = 8/8 = 1 x₂ = (3 - 5) / 8 = -2/8 = -1/4

2. 6x² + 7x - 5 = 0

a = 6, b = 7, c = -5

x = (-7 ± √(7² - 4 * 6 * (-5))) / (2 * 6)

x = (-7 ± √(49 + 120)) / 12

x = (-7 ± √169) / 12

x = (-7 ± 13) / 12

So, we have two solutions:

x₁ = (-7 + 13) / 12 = 6/12 = 1/2 x₂ = (-7 - 13) / 12 = -20/12 = -5/3

3. 18x² - 9x - 5 = 0

a = 18, b = -9, c = -5

x = (-(-9) ± √((-9)² - 4 * 18 * (-5))) / (2 * 18)

x = (9 ± √(81 + 360)) / 36

x = (9 ± √441) / 36

x = (9 ± 21) / 36

So, we have two solutions:

x₁ = (9 + 21) / 36 = 30/36 = 5/6 x₂ = (9 - 21) / 36 = -12/36 = -1/3

These are the solutions to the given quadratic equations.