Question

Помогите, пожалуйста, решить уравнения!!! 1) х² = -4х 2) 5х² = -2х 3) 4х² + 3х = 0 4) 36х² = 1 5) 2х²-14=0 6) х²-6х=0 7) 3х²-75=0 8) 12-х²=1 9) 5х=2=2-2х² 10) х²-6х=4х-25 Заранее спасибо!!!)

Answer 1

1) x² + 4x = 0
x(x + 4) = 0
x = 0 или x + 4 = 0
                x = -4
Ответ: 0; -4
2) 5х² + 2х = 0
x(5x + 2) = 0
x = 0 или 5x + 2 = 0
                 5x = -2
                 x = -2/5
Ответ: 0; -2/5
3) 4х² + 3х = 0
x(4x + 3) = 0
x = 0 или 4x + 3 = 0
                 4x = -3
                 x = -3/4
Ответ: 0; -3/4
4) 36х² = 1
    36х² - 1 = 0
(6x + 1) * (6x - 1) = 0
x = +- 1/6
Ответ: 1/6; -1/6
5) 2х² - 14 = 0
    2(x² - 7) = 0
    x² = 7
    x = +-√7
Ответ: √7; -√7
6) х² - 6х = 0
x(x - 6) = 0
x = 0 или x - 6 = 0
                x = 6
Ответ: 0; 6 
7) 3х² - 75 = 0
3(x² - 25) = 0
   x² = 25
   x = +-5
Ответ: 5; -5
8) 12 - х² = 1
11 - x² = 0
x² - 11 = 0
x² = 11
x = +-√11
Ответ: √11; -√11
9) Некорректно написано уравнение, проверьте условие
10) х² - 6х = 4х - 25
x² - 10x + 25 = 0
D = 10² - 4*25 = 0, D = 0 ⇒ один корень
х = 10/2 = 5
Ответ: 5

Answer 2

1) x² = -4x To solve this equation, we can rearrange it to the form x² + 4x = 0, and then factor out x to get x(x + 4) = 0. So the solutions are x = 0 and x = -4.

2) 5x² = -2x + 3 First, we rearrange the equation to the form 5x² + 2x - 3 = 0. Then we can use the quadratic formula to find the solutions: x = (-2 ± √(2² - 4*5*(-3))) / (2*5) x = (-2 ± √(4 + 60)) / 10 x = (-2 ± √64) / 10 x = (-2 ± 8) / 10 So the solutions are x = (-2 + 8) / 10 = 6 / 10 = 0.6 and x = (-2 - 8) / 10 = -10 / 10 = -1.

3) 4x² + 3x = 0 We can factor out x to get x(4x + 3) = 0, so the solutions are x = 0 and 4x + 3 = 0, which gives us x = -3/4.

4) 36x² = 1 We can solve for x by taking the square root of both sides: x = ±√(1/36) x = ± 1/6

5) 2x² - 14 = 0 First, we add 14 to both sides: 2x² = 14 Then, divide by 2: x² = 7 Take the square root: x = ±√7

6) x² - 6x = 0 Factor out x: x(x - 6) = 0 So the solutions are x = 0 and x - 6 = 0, which gives us x = 6.

7) 3x² - 75 = 0 Add 75 to both sides: 3x² = 75 Divide by 3: x² = 25 Take the square root: x = ±5

8) 12 - x² = 1 Subtract 1 from both sides: 12 - 1 - x² = 0 Rearrange: x² = 11 Take the square root: x = ±√11

9) 5x = 2 - 2x² Add 2x² to both sides: 2x² + 5x = 2 Rearrange: 2x² + 5x - 2 = 0 Use the quadratic formula to find the solutions.

10) x² - 6x = 4x - 25 Rearrange: x² - 6x - 4x + 25 = 0 Combine like terms: x² - 10x + 25 = 0 Factor: (x - 5)(x - 5) = 0 So the only solution is x = 5.