Question

1. (2х – 3)2 – (7 – 2х)2 = 2 2. (8 – 9а)∙а = - 40 + (6 – 3а)∙(6 + 3а) 3. 24 –( 3у + 1)∙( 4у – 5) = (11 – 6у)∙(2у – 7) 4. ( х + 6)2 – (х -5)∙(х + 5) = 79

Answer 1

Ответ:1) (2x-3)2-(7-2x)2=2

4x-6-(14-4)=2

4x-6-14+4=2

8x-20=2

8x=20+2

x=22

x=11/4

Объяснение:

Answer 2

Let's solve these equations one by one:

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

To solve this equation, we'll first expand both sides:

(4x^2 - 12x + 9) - ((7 - 2x)(7 - 2x)) = 2

Now, expand the right side:

4x^2 - 12x + 9 - (49 - 14x + 4x^2) = 2

Now, simplify the equation:

4x^2 - 12x + 9 - 49 + 14x - 4x^2 = 2

Combine like terms:

-40 = 2

This equation is inconsistent because -40 is not equal to 2. Therefore, there are no solutions.

2. (8 - 9a)∙a = -40 + (6 - 3a)∙(6 + 3a)

First, expand both sides:

8a - 9a^2 = -40 + (6 * 6 - 3a * 3a)

Simplify:

-9a^2 + 8a = -40 + (36 - 9a^2)

Now, let's isolate the terms with "a" on one side:

-9a^2 + 8a + 9a^2 = -40 + 36

The -9a^2 and 9a^2 terms cancel out:

8a = -4

Now, divide by 8 to solve for "a":

a = -4 / 8 a = -1/2

So, the solution to this equation is a = -1/2.

3. 24 - (3y + 1)∙(4y - 5) = (11 - 6y)∙(2y - 7)

First, expand both sides:

24 - (12y^2 - 17y - 3y + 5) = (22y - 12y^2) - 14y^2 + 77y - 22

Simplify:

24 - 12y^2 + 17y - 5 = -14y^2 + 77y - 22

Combine like terms:

-12y^2 + 17y + 19 = -14y^2 + 77y - 22

Now, let's isolate the terms with "y" on one side:

-12y^2 + 17y + 14y^2 - 77y + 19 + 22 = 0

Combine like terms:

2y^2 - 60y + 41 = 0

Now, you can use the quadratic formula to solve for "y":

y = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -60, and c = 41:

y = (-(-60) ± √((-60)^2 - 4 * 2 * 41)) / (2 * 2)

y = (60 ± √(3600 - 328)) / 4

y = (60 ± √3272) / 4

Since √3272 is not a nice whole number, the solutions for "y" will involve square roots:

y = (60 ± √3272) / 4

4. (x + 6)^2 - (x - 5) * (x + 5) = 79

First, expand both sides:

(x^2 + 12x + 36) - (x^2 - 25) = 79

Now, simplify the equation:

x^2 + 12x + 36 - x^2 + 25 = 79

Combine like terms:

12x + 61 = 79

Now, isolate the term with "x" on one side:

12x = 79 - 61

12x = 18

Now, divide by 12 to solve for "x":

x = 18 / 12 x = 3/2

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