Question

1)(x+2)(x-2)-x(x-6)=0 2)3x(4x+12x)-(6x-1)(6x+1)=11x 3)(x+7)(x-7)-(3x-1)(x+1)=4-2x^2

Answer 1

Ответ:

1) (x+2)(x-2)-x(x-6)=0

раскроем скобки  

x2-2x+2x-4-x2+6x = 0

6x-4 = 0  

6x = 4

x  = $\frac{4}{6}$  

x  = $\frac{2}{3}$

2) 3x(4x+12x)-(6x-1)(6x+1)=11x

раскроем скобки  

12x2+36x2-36x2-6x+6x+1 = 11x

12x2-11x+1 = 0  

Вычислим дискриминант D

D = b2 - 4ac = ( – 11)2 – 4·12·( + 1) = 73

x1   =  11 + √ 73

              24

x2 =  11 – √ 73

             24

3)(x+7)(x-7)-(3x-1)(x+1)=4-2x2

раскроем скобки  

x2-7x+7x-49-3x2-3x+x+1 = 4-2x2

-2x-52 = 0  

2x+52 = 0

2x = -52

x = -26

Пошаговое объяснение:

Answer 2

Let's solve each of these equations step by step:

1. (x+2)(x-2) - x(x-6) = 0

First, expand and simplify both sides of the equation:

(x^2 - 4) - (x^2 - 6x) = 0

Now, distribute the negative sign on the second term:

x^2 - 4 - x^2 + 6x = 0

Now, combine like terms:

6x - 4 = 0

Add 4 to both sides:

6x = 4

Now, divide both sides by 6 to isolate x:

x = 4/6

Simplify the fraction:

x = 2/3

So, the solution to this equation is x = 2/3.

2. 3x(4x+12x) - (6x-1)(6x+1) = 11x

First, simplify both sides of the equation:

3x(16x) - (36x^2 - 1) = 11x

Now, distribute the 3x on the left side:

48x^2 - (36x^2 - 1) = 11x

Now, distribute the negative sign on the right side:

48x^2 - 36x^2 + 1 = 11x

Combine like terms on the left side:

12x^2 + 1 = 11x

Now, move all terms to one side to set the equation to zero:

12x^2 - 11x + 1 = 0

This is a quadratic equation. You can solve it using the quadratic formula:

x = [-b ± √(b^2 - 4ac)] / (2a)

In this case, a = 12, b = -11, and c = 1. Plug these values into the formula:

x = [-(-11) ± √((-11)^2 - 4(12)(1))] / (2(12))

x = (11 ± √(121 - 48)) / 24

x = (11 ± √73) / 24

So, the solutions to this equation are:

x = (11 + √73) / 24 x = (11 - √73) / 24

3. (x+7)(x-7) - (3x-1)(x+1) = 4 - 2x^2

First, expand and simplify both sides of the equation:

(x^2 - 49) - (3x^2 + 2x - 1) = 4 - 2x^2

Now, distribute the negative sign on the right side:

x^2 - 49 - 3x^2 - 2x + 1 = 4 - 2x^2

Combine like terms on both sides:

-x^2 - 2x - 48 = 4 - 2x^2

Now, move all terms to one side to set the equation to zero:

-x^2 - 2x - 48 - 4 + 2x^2 = 0

Simplify:

-x^2 - 52 = 0

Multiply the equation by -1 to make it easier to work with:

x^2 + 52 = 0

This is a quadratic equation. You can solve it using the quadratic formula:

x = [-b ± √(b^2 - 4ac)] / (2a)

In this case, a = 1, b = 0, and c = 52. Plug these values into the formula:

x = [0 ± √(0 - 4(1)(52))] / (2(1))

x = [0 ± √(-208)] / 2

Since the discriminant (the value inside the square root) is negative, there are no real solutions to this equation. The solutions are complex numbers:

x = ±√(208)i / 2

So, the solutions are:

x = (√208)i / 2 x = (-√208)i / 2