Question

3) (x + 7)(x-7)-(3x-1)(x+1)=4-2x²

Answer 1

Ответ:(-2x-52=0\)

Объяснение:

Answer 2

Let's simplify the given equation step by step:

1. Expand the expressions on both sides of the equation:

On the left side: (x + 7)(x - 7) = x^2 - 49 (Using the difference of squares formula: (a - b)(a + b) = a^2 - b^2)

-(3x - 1)(x + 1) = -(3x^2 - x - 3x + 1) = -(3x^2 - 4x + 1)

So, the left side of the equation becomes: x^2 - 49 - (-3x^2 + 4x - 1) = x^2 - 49 + 3x^2 - 4x + 1

2. Combine like terms on the left side: x^2 + 3x^2 - 4x - 49 + 1 = 4 - 2x^2

3. Combine like terms on both sides of the equation: 4x^2 - 4x - 48 = 4 - 2x^2

4. Move all terms to one side of the equation: 4x^2 - 2x^2 - 4x - 48 - 4 = 0

5. Combine like terms on the left side: 2x^2 - 4x - 52 = 0

6. Divide the entire equation by 2 to simplify it: x^2 - 2x - 26 = 0

Now, you have a quadratic equation in standard form. You can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -2, and c = -26. Plug these values into the formula:

x = (-(-2) ± √((-2)² - 4(1)(-26))) / (2(1)) x = (2 ± √(4 + 104)) / 2 x = (2 ± √108) / 2 x = (2 ± 2√27) / 2

Now, you can simplify further:

x = 2/2 ± 2√27/2 x = 1 ± √27

So, the solutions to the equation are: x₁ = 1 + √27 x₂ = 1 - √27

You can simplify √27 further if needed: √27 = √(9 * 3) = 3√3

So, the solutions are: x₁ = 1 + 3√3 x₂ = 1 - 3√3