Question

X^2 -1 >0решите неравенство.​

Answer 1

x² - 1 > 0

(x - 1)(x + 1) > 0

         +                    -                        +

_________₀___________₀__________

                 - 1                        1

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Ответ : x ∈ (- ∞ ; - 1) ∪ (1 ; + ∞)

Answer 2

To solve the inequality $x^2 - 1 > 0$, we need to find the values of $x$ that satisfy the inequality. Let's break it down step by step:

Step 1: Factor the quadratic expression $x^2 - 1$. $x^2 - 1 = (x+1)(x-1)$

Step 2: Set each factor to zero to find the critical points: $x + 1 = 0$ --> $x = -1$ $x - 1 = 0$ --> $x = 1$

Step 3: Create a sign chart to determine the intervals where the inequality holds true:

Interval	$x + 1$	$x - 1$	$x^2 - 1$
$x < -1$	-	-	+
$-1 < x < 1$	+	-	-
$x > 1$	+	+	+

Step 4: Identify the solution: From the sign chart, we can see that the inequality $x^2 - 1 > 0$ is true for $x < -1$ and $x > 1$.

So, the solution to the inequality is: $x < -1$ or $x > 1$