Question

Решите уравнения:a) (x-2)^2-x^2=12b)(2x+3)^2-4(x-1) (x+1) =49​

Answer 1

(x-2)^2-x^2=12
x^2-4x+4-x^2=12
-4x+4=12
-4x=12-4
-4x=8
x=-2

Answer 2

a) (x-2)^2 - x^2 = 12

Let's solve this equation step by step:

1. Expand the left side of the equation: (x^2 - 4x + 4) - x^2 = 12

2. Simplify the equation by canceling out x^2 on both sides: -4x + 4 = 12

3. Subtract 4 from both sides of the equation: -4x = 12 - 4 -4x = 8

4. Divide both sides by -4 to solve for x: x = 8 / (-4) x = -2

So, the solution to the equation is x = -2.

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

Let's solve this equation step by step:

1. Expand both sides of the equation: (4x^2 + 12x + 9) - (4x^2 - 4) = 49

2. Simplify the equation by distributing the negative sign on the right side: 4x^2 + 12x + 9 - 4x^2 + 4 = 49

3. Combine like terms on the left side of the equation: 12x + 13 = 49

4. Subtract 13 from both sides of the equation: 12x = 49 - 13 12x = 36

5. Divide both sides by 12 to solve for x: x = 36 / 12 x = 3

So, the solution to the equation is x = 3.