Question

3) (12 + x)²>x² + 21x​

Answer 1

Ответ:

(12 + x)²>x² + 21x

144 + 24х + x² > x² + 21x

3х > 144

х > 48

Answer 2

To solve the inequality (12 + x)² > x² + 21x, you can follow these steps:

1. Expand both sides of the inequality: (12 + x)² > x² + 21x

   (12 + x)(12 + x) > x² + 21x

   144 + 12x + 12x + x² > x² + 21x

2. Simplify the left side by combining like terms: 144 + 24x + x² > x² + 21x

3. Subtract x² and 21x from both sides to isolate the x² term on the left side: 144 + 24x + x² - x² - 21x > x² + 21x - x² - 21x

   144 + 3x > 0

4. Now, subtract 144 from both sides to further isolate the x term: 144 + 3x - 144 > 0 - 144

   3x > -144

5. Finally, divide both sides by 3 to solve for x: (3x)/3 > (-144)/3

   x > -48

So, the solution to the inequality is x > -48.