Question

5(x-3)(x+5)-(x-8)²>21​

Answer 1

Ответ:

.......................

Answer 2

To solve the inequality 5(x-3)(x+5)-(x-8)² > 21, you can follow these steps:

1. Expand the expressions:

   5(x-3)(x+5) = 5(x²+5x-3x-15) = 5(x²+2x-15)

   (x-8)² = x²-16x+64

2. Rewrite the inequality with the expanded expressions:

   5(x²+2x-15) - (x²-16x+64) > 21

3. Distribute the 5 on the left side:

   5x² + 10x - 75 - x² + 16x - 64 > 21

4. Combine like terms on the left side:

   4x² + 26x - 75 - 64 > 21

5. Simplify further:

   4x² + 26x - 139 > 21

6. Move 21 to the left side by subtracting it:

   4x² + 26x - 139 - 21 > 0

7. Combine constants:

   4x² + 26x - 160 > 0

8. Now, you need to find the values of x that satisfy this inequality. You can do this by finding the roots (zeros) of the corresponding equation:

   4x² + 26x - 160 = 0

You can solve this quadratic equation for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 4, b = 26, and c = -160.

x = (-26 ± √(26² - 4 * 4 * (-160))) / (2 * 4)

Now, calculate the discriminant (the value inside the square root):

Discriminant = b² - 4ac = 26² - 4 * 4 * (-160)

Discriminant = 676 + 2560 = 3236

Now, plug the discriminant back into the quadratic formula:

x = (-26 ± √3236) / (2 * 4)

x = (-26 ± 2√809) / 8

Now, you have two possible solutions:

1. x = (-26 + 2√809) / 8
2. x = (-26 - 2√809) / 8

These are the values of x that satisfy the inequality 5(x-3)(x+5)-(x-8)² > 21. However, you should also check the sign of the expression 4x² + 26x - 160 for each of these values to determine which intervals of x make the inequality true.