Question

1) (7 − 8x)(2x + 1) + (4x − 1)² = 0; 2) (2x − 5)² – (2x − 3)(2x + 3) = 15 3) (3x + 5)(3x - 5)-(3x - 1)² = −4 4) (9x + 2)(1 - 4x) + (5-6x)² = -8​

Answer 1

Ответ:

1) (7-8х)(2х+1)+(4х-1)²=0

Answer 2

To solve these equations, we will simplify and solve each one step by step. Let's start with the first equation:

1. (7 - 8x)(2x + 1) + (4x - 1)² = 0

First, expand the expressions:

(7 - 8x)(2x + 1) = 14x² - 8x² + 7 - 8x (4x - 1)² = 16x² - 8x + 1

Now, substitute these back into the original equation:

(14x² - 8x² + 7 - 8x) + (16x² - 8x + 1) = 0

Combine like terms:

14x² - 8x² + 7 - 8x + 16x² - 8x + 1 = 0

Combine the x² terms:

30x² - 16x² - 8x - 8x + 7 + 1 = 0

Combine like terms again:

14x² - 16x - 1 = 0

Now, we have a quadratic equation. Let's solve it using the quadratic formula:

a = 14, b = -16, and c = -1

The quadratic formula is:

x = (-b ± √(b² - 4ac)) / (2a)

Plug in the values:

x = (-(-16) ± √((-16)² - 4 * 14 * (-1))) / (2 * 14)

x = (16 ± √(256 + 56)) / 28

x = (16 ± √312) / 28

Now, you can simplify further:

x = (16 ± 2√78) / 28

x = (8 ± √78) / 14

So, the solutions to the first equation are:

x = (8 + √78) / 14 x = (8 - √78) / 14

Now, let's move on to the second equation:

2. (2x - 5)² - (2x - 3)(2x + 3) = 15

First, expand the expressions:

(2x - 5)² = 4x² - 20x + 25 (2x - 3)(2x + 3) = 4x² - 9

Now, substitute these back into the original equation:

(4x² - 20x + 25) - (4x² - 9) = 15

Simplify:

4x² - 20x + 25 - 4x² + 9 = 15

Combine like terms:

-20x + 25 + 9 = 15

-20x + 34 = 15

Now, isolate x:

-20x = 15 - 34

-20x = -19

x = (-19)/(-20)

x = 19/20

So, the solution to the second equation is:

x = 19/20

Now, let's move on to the third equation:

3. (3x + 5)(3x - 5) - (3x - 1)² = -4

First, expand the expressions:

(3x + 5)(3x - 5) = 9x² - 25 (3x - 1)² = 9x² - 6x + 1

Now, substitute these back into the original equation:

(9x² - 25) - (9x² - 6x + 1) = -4

Simplify:

9x² - 25 - 9x² + 6x - 1 = -4

Combine like terms:

6x - 26 = -4

Now, isolate x:

6x = -4 + 26

6x = 22

x = 22/6

x = 11/3

So, the solution to the third equation is:

x = 11/3

Finally, let's solve the fourth equation:

4. (9x + 2)(1 - 4x) + (5 - 6x)² = -8

First, expand the expressions:

(9x + 2)(1 - 4x) = 9x - 36x² + 2 - 8x (5 - 6x)² = 25 - 60x + 36x²

Now, substitute these back into the original equation:

(9x - 36x² + 2 - 8x) + (25 - 60x + 36x²) = -8

Simplify:

9x - 36x² + 2 - 8x + 25 - 60x + 36x² = -8

Combine like terms:

(9x - 8x) + (-36x² + 36x²) + (2 + 25) - 60x = -8

x - 60x + 27 = -8

Combine like terms again:

-59x + 27 = -8

Now, isolate x:

-59x = -8 - 27

-59x = -35

x = (-35)/(-59)

x = 35/59

So, the solution to the fourth equation is:

x = 35/59

To summarize:

1. x = (8 + √78) / 14, x = (8 - √78) / 14
2. x = 19/20
3. x = 11/3
4. x = 35/59