32.20. 1) (x + 9)(x - 2) - (x - 2)² > 0; 3) (5-x)(x + 5) + (x - 5)²>0; 2) (10-x)² + (x+10)(10-x) < 0; 4) (4+x)(2-x)+(1-x)² > 0.пожалуйста полностью сделайте 7 класс алгебра ​

Ответ:

Let's solve each inequality one by one:

1) (x + 9)(x - 2) - (x - 2)² > 0:

Expanding the equation, we get:

(x^2 - 2x + 9x - 18) - (x^2 - 4x + 4) > 0

Simplifying further:

(7x - 18) - (4x - 4) > 0

3x - 14 > 0

3x > 14

x > 14/3

Therefore, the solution to this inequality is x > 14/3.

2) (10-x)² + (x+10)(10-x) < 0:

Expanding the equation:

(100 - 20x + x²) + (10x - x² + 100 - 10x) < 0

Simplifying further:

200 - 20x < 0

-20x < -200

x > 10

Therefore, the solution to this inequality is x > 10.

3) (5-x)(x + 5) + (x - 5)² > 0:

Expanding the equation:

(25 - 5x + 5x - x²) + (x² - 10x + 25) > 0

Simplifying further:

50 - 2x² > 0

-2x² > -50

x² < 25

x < 5 or x > -5

Therefore, the solution to this inequality is x < 5 or x > -5.

4) (4+x)(2-x) + (1-x)² > 0:

Expanding the equation:

(8 - 4x + 2x - x²) + (1 - 2x + x²) > 0

Simplifying further:

9 - 4x > 0

-4x > -9

x < 9/4

Therefore, the solution to this inequality is x < 9/4.

In summary:

1) x > 14/3

2) x > 10

3) x < 5 or x > -5

4) x < 9/4