Question

РЕШИТЕ!!!!!!!!!!!!!!!x^2⩾16

Answer 1

X^2⩾16
Извлекаем квадратный корень
|x|⩾4
Рассмотрим все возможные случаи
x⩾4, x⩾0
-x⩾4, x<0
Решаем
x принадлежит [4,+ бесконечность)
x принадлежит (- бесконечность,-4]

x принадлежит (- бесконечность,-4] обьединение [4,+ бесконечность)

Answer 2

To solve the inequality x^2 ≥ 16, we need to find the values of x that satisfy the inequality. Let's break it down step by step:

Step 1: Factor the left side of the inequality, if possible. x^2 - 16 ≥ 0

Step 2: Now, we can factor the left side as the difference of squares: (x + 4)(x - 4) ≥ 0

Step 3: Identify the critical points where the left side changes sign, i.e., where (x + 4)(x - 4) = 0. These critical points are x = -4 and x = 4.

Step 4: Create a sign chart to check the sign of the expression (x + 4)(x - 4) in each interval separated by the critical points.

The intervals are:

1. x < -4
2. -4 < x < 4
3. x > 4

Step 5: Test a value in each interval to determine the sign of the expression.

For x = -5 (interval 1): (-5 + 4)(-5 - 4) = (-1)(-9) = 9, which is positive.

For x = 0 (interval 2): (0 + 4)(0 - 4) = (4)(-4) = -16, which is negative.

For x = 5 (interval 3): (5 + 4)(5 - 4) = (9)(1) = 9, which is positive.

Step 6: Determine the solution based on the sign chart. The inequality (x + 4)(x - 4) ≥ 0 is satisfied when x is in the intervals where the expression is greater than or equal to zero. So, the solution is:

x ≤ -4 or x ≥ 4

In interval notation: (-∞, -4] ∪ [4, ∞)