Question

(x^2-8)=0 решите неравенство.

Answer 1

±корень из 8 вот так

Answer 2

To solve the inequality $x^2 - 8 \geq 0$, we first find the critical points by setting the expression inside the inequality to zero and then determining the sign of the expression in different intervals.

Step 1: Find critical points: Set $x^2 - 8 = 0$, $x^2 = 8$, $x = \pm \sqrt{8} \approx \pm 2.83$.

Step 2: Test intervals: We test three intervals: $(- \infty, -2.83)$, $(-2.83, 2.83)$, and $(2.83, \infty)$. We can pick any value within each interval to check the sign of the expression $x^2 - 8$.

For $x = -3$, $x^2 - 8 = (-3)^2 - 8 = 9 - 8 = 1 > 0$. For $x = 0$, $x^2 - 8 = 0^2 - 8 = -8 < 0$. For $x = 3$, $x^2 - 8 = 3^2 - 8 = 9 - 8 = 1 > 0$.

Step 3: Analyze the results: From the tests, we see that the inequality $x^2 - 8 \geq 0$ is true for the intervals $(- \infty, -2.83)$ and $(2.83, \infty)$.

Step 4: Write the solution: The solution to the inequality is given by the intervals where $x^2 - 8 \geq 0$: $x \in (-\infty, -2.83] \cup [2.83, \infty).$