Question

(x² – 2x + 6)(x – 4) > 0);(3х + 6) —3x° — 3х – 4) < 0;​

Answer 1

Объяснение:

это первое, во втором что то не то написано

Answer 2

To solve the inequalities, you can follow these steps:

1. Solve the first inequality: (x² - 2x + 6)(x - 4) > 0

First, find the roots of the quadratic equation x² - 2x + 6 = 0 using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = -2, and c = 6:

x = (2 ± √((-2)² - 4(1)(6))) / (2(1)) x = (2 ± √(4 - 24)) / 2 x = (2 ± √(-20)) / 2

Since the discriminant (√(-20)) is imaginary, the quadratic has no real roots. This means the quadratic is always positive or always negative.

Now, consider the factors of the quadratic expression (x² - 2x + 6)(x - 4):

1. x² - 2x + 6 is always positive (no real roots).
2. (x - 4) is positive when x > 4 and negative when x < 4.

To find where the expression (x² - 2x + 6)(x - 4) > 0, you need to analyze the signs of the factors and their combinations.

• When x > 4, both factors are positive, so the expression is positive.
• When x < 4, the first factor is positive, but the second factor is negative, so the expression is negative.

So, the solution to the first inequality is:

x < 4.

2. Solve the second inequality: (3x + 6) - (3x² - 3x - 4) < 0

Simplify the inequality:

3x + 6 - 3x² + 3x + 4 < 0

Now, simplify further:

-3x² + 10 < 0

To find where -3x² + 10 < 0, you need to analyze the sign of -3x² + 10. First, find the roots of -3x² + 10:

-3x² + 10 = 0

Divide both sides by -3:

x² - 10/3 = 0

Now, find the roots using the quadratic formula:

x = ±√(10/3)

The roots are imaginary since the discriminant is negative, meaning the quadratic doesn't have real roots.

Now, consider the expression -3x² + 10:

-3x² + 10 is always positive (no real roots).

Since the expression is always positive, the solution to the second inequality is:

For all real values of x.

In summary:

1. (x² - 2x + 6)(x - 4) > 0 has the solution x < 4.
2. (3x + 6) - (3x² - 3x - 4) < 0 has the solution for all real values of x.