Question

1) (10 + x)(100 - 10x + x²) -x³-500x<0; 2) -x³ +675x - (15 + x)(225 - 15x + x) > 0;3) (169 + 13x +x²)(x - 13) - x³- 2262x больше либо равно 0;4) 1331x - x³+ (11 + x)(x² - 11x + 121) >0.​

Answer 1

Ответ:

см вложение

Объяснение:

Answer 2

Let's simplify each of the given expressions:

1. (10 + x)(100 - 10x + x²) - x³ - 500x < 0

Expanding the brackets, we have:

(10 + x)(100 - 10x + x²) - x³ - 500x = (10 + x)(x² - 10x + 100) - x³ - 500x = (10x² - 100x + 1000 + x³ - 10x² + 100x) - x³ - 500x = -x³ + 1000 - x³ - 500x = -2x³ - 500x + 1000

Now, we need to solve the inequality -2x³ - 500x + 1000 < 0.

2. -x³ + 675x - (15 + x)(225 - 15x + x) > 0

Expanding the brackets, we have:

-x³ + 675x - (15 + x)(225 - 15x + x) = -x³ + 675x - (15 + x)(225 - 14x) = -x³ + 675x - (3375 - 225x + 15x - x²) = -x³ + 675x - 3375 + 225x - 15x + x² = x² - x³ + 885x - 3375

Now, we need to solve the inequality x² - x³ + 885x - 3375 > 0.

3. (169 + 13x + x²)(x - 13) - x³ - 2262x ≥ 0

Expanding the brackets, we have:

(169 + 13x + x²)(x - 13) - x³ - 2262x = (169x - 2197 + 13x² - 169x + x³ - 13x²) - x³ - 2262x = -2197 - x³ - 2262x

Now, we need to solve the inequality -2197 - x³ - 2262x ≥ 0.

4. 1331x - x³ + (11 + x)(x² - 11x + 121) > 0

Expanding the brackets, we have:

1331x - x³ + (11 + x)(x² - 11x + 121) = 1331x - x³ + (11x² - 121x + 1331 + x³ - 11x² + 121x) = 1331x - x³ + x³ + 1331x = 2662x

Now, we need to solve the inequality 2662x > 0.

Please let me know if you'd like help solving any of these inequalities.