Question

Решить неравенство x^2>9

Answer 1

X1>3
x2>-3
Ответ:(-3;3)

Answer 2

To solve the inequality $x^2 > 9$, we need to find the values of $x$ that satisfy the inequality. The steps are as follows:

Step 1: Set up the inequality: $x^2 > 9$

Step 2: Rewrite the inequality in a way that one side is zero: $x^2 - 9 > 0$

Step 3: Factor the expression on the left side: $(x - 3)(x + 3) > 0$

Step 4: Find the critical points where the expression equals zero: Setting each factor to zero and solving for $x$: $(x - 3) = 0 \quad \text{gives} \quad x = 3$ $(x + 3) = 0 \quad \text{gives} \quad x = -3$

Step 5: Create a sign chart to determine the sign of the expression in each interval:

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Intervals:       (-∞, -3)   |   (-3, 3)   |   (3, ∞)
Test Value:         -4       |      0      |      4
Expression:   (+)(-)  > 0  |   (-)(-)  > 0   |   (+)(+)  > 0

Step 6: Analyze the sign chart and find the solution: In the interval $(-∞, -3)$, the expression $(x - 3)(x + 3) > 0$ is positive. In the interval $(-3, 3)$, the expression $(x - 3)(x + 3) < 0$ is negative. In the interval $(3, ∞)$, the expression $(x - 3)(x + 3) > 0$ is positive.

Step 7: Write the solution as an inequality: The solution to the inequality $x^2 > 9$ is $x \in (-\infty, -3) \cup (3, \infty)$. In interval notation, this can be written as $(-∞, -3) \cup (3, ∞)$. This means that any value of $x$ less than -3 or greater than 3 will satisfy the original inequality.