Question

Решить уравнение x² = 7 x² = 11 x² + 6x = 0 x² + 5x = 0 x² = 8x x² = 12x

Answer 1

Ответ:

$x {}^{2} = 7 \\ x \sqrt{7 } \\ x = - \sqrt{7} \\ x = \sqrt{7}$

Answer 2

Let's solve each equation step by step:

1. x² = 7 To solve for x, we can take the square root of both sides: x = ±√7 So the solutions are x = √7 and x = -√7.

2. x² = 11 Again, taking the square root of both sides: x = ±√11 The solutions are x = √11 and x = -√11.

3. x² + 6x = 0 Factor out x from the left side: x(x + 6) = 0 Now, set each factor to zero and solve for x:

1. x = 0
2. x + 6 = 0 x = -6 The solutions are x = 0 and x = -6.

4. x² + 5x = 0 Factor out x from the left side: x(x + 5) = 0 Now, set each factor to zero and solve for x:

1. x = 0
2. x + 5 = 0 x = -5 The solutions are x = 0 and x = -5.

5. x² = 8x Move all terms to one side of the equation: x² - 8x = 0 Factor out x from the left side: x(x - 8) = 0 Now, set each factor to zero and solve for x:

1. x = 0
2. x - 8 = 0 x = 8 The solutions are x = 0 and x = 8.

6. x² = 12x Move all terms to one side of the equation: x² - 12x = 0 Factor out x from the left side: x(x - 12) = 0 Now, set each factor to zero and solve for x:

1. x = 0
2. x - 12 = 0 x = 12 The solutions are x = 0 and x = 12.

To summarize the solutions for each equation:

1. x = √7 and x = -√7
2. x = √11 and x = -√11
3. x = 0 and x = -6
4. x = 0 and x = -5
5. x = 0 and x = 8
6. x = 0 and x = 12