Question

X2-8x-33 больше или ровно 0

Answer 1

Ответ:

x∈(-∞;-3]∪[11;+∞)

Пошаговое объяснение:

x²-8x-33≥0

D=b²-4ac =(-8)²-4·1·(-33)=64+132=196

x₁=-3  x₂=11

x∈(-∞;-3]∪[11;+∞)

Answer 2

To find the values of x for which the expression x^2 - 8x - 33 is greater than or equal to 0, we need to solve the inequality:

x^2 - 8x - 33 ≥ 0

To do this, we can find the critical points where the expression is equal to zero, and then analyze the sign of the expression in the intervals formed by these critical points.

Step 1: Find the critical points (where the expression equals zero):

x^2 - 8x - 33 = 0

To factor or solve the quadratic equation, we can use the quadratic formula:

x = [ -b ± √(b^2 - 4ac) ] / 2a

where the quadratic equation is in the form ax^2 + bx + c = 0.

For our equation, a = 1, b = -8, and c = -33.

x = [ -(-8) ± √((-8)^2 - 4 * 1 * (-33)) ] / 2 * 1

x = [ 8 ± √(64 + 132) ] / 2

x = [ 8 ± √196 ] / 2

x = [ 8 ± 14 ] / 2

Now, we have two critical points:

1. x = (8 + 14) / 2 = 22 / 2 = 11
2. x = (8 - 14) / 2 = -6 / 2 = -3

Step 2: Analyze the sign of the expression in different intervals:

We have three intervals to consider: (-∞, -3), (-3, 11), and (11, ∞).

Choose a test point from each interval and evaluate the expression to determine its sign in that interval:

1. Let's choose x = -4 (from the interval -∞ to -3):

x^2 - 8x - 33 = (-4)^2 - 8(-4) - 33 = 16 + 32 - 33 = 15 (positive)

2. Let's choose x = 0 (from the interval -3 to 11):

x^2 - 8x - 33 = (0)^2 - 8(0) - 33 = -33 (negative)

3. Let's choose x = 12 (from the interval 11 to ∞):

x^2 - 8x - 33 = (12)^2 - 8(12) - 33 = 144 - 96 - 33 = 15 (positive)

Step 3: Determine the solution:

We want to find where x^2 - 8x - 33 ≥ 0.

From the analysis above, we see that the expression is non-negative (greater than or equal to zero) in the intervals (-∞, -3) and (11, ∞).

Therefore, the solution to the inequality x^2 - 8x - 33 ≥ 0 is:

x ∈ (-∞, -3] ∪ [11, ∞)