Question

X ^ 2 > 16 - розв'язати нерівність​

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

x^2 - 16 = (x + 4)(x - 4) = 0

Тому, x = -4 або x = 4.

Ці точки ділять числову пряму на три інтервали: (-∞, -4), (-4, 4), та (4, +∞). Якщо x^2 > 16, то значення x має лежати на інтервалах (-∞, -4) та (4, +∞):

x < -4 або x > 4

Отже, розв'язок нерівності x^2 > 16 складається з двох інтервалів: (-∞, -4) та (4, +∞).

Answer 3

To solve the inequality $x^2 > 16$, we can follow these steps:

Step 1: Subtract 16 from both sides of the inequality to isolate the $x^2$ term: $x^2 - 16 > 0$

Step 2: Factor the left side of the inequality, which is a difference of squares: $(x - 4)(x + 4) > 0$

Step 3: Determine the sign of the expression $(x - 4)(x + 4)$ for different ranges of $x$. We can do this by considering the signs of the factors $(x - 4)$ and $(x + 4)$.

When $x < -4$: Both factors are negative, so the product is positive: $(x - 4)(x + 4) > 0$.

When $-4 < x < 4$: The factor $(x - 4)$ is negative, while $(x + 4)$ is positive. Hence, the product is negative: $(x - 4)(x + 4) < 0$.

When $x > 4$: Both factors are positive, so the product is positive: $(x - 4)(x + 4) > 0$.

Step 4: Write the solution in interval notation based on the sign analysis above. The solution is the set of values for $x$ where the inequality is true, which is when $(x - 4)(x + 4) > 0$.

Therefore, the solution to the inequality $x^2 > 16$ is $-\infty < x < -4$ or $4 < x < \infty$ in interval notation.