Question

X²-7x-30>0 решить неравенство

Answer 1

Ответ:

Х больше - 6

Объяснение:

Answer 2

To solve the inequality $x^2 - 7x - 30 > 0$, we'll follow these steps:

Step 1: Factorize the quadratic expression. Step 2: Find the critical points by setting the expression to zero and solving for $x$. Step 3: Determine the sign of the expression in the intervals created by the critical points. Step 4: Identify the solution range for which the expression is greater than zero.

Let's proceed with the steps:

Step 1: Factorize the quadratic expression $x^2 - 7x - 30 > 0$: $x^2 - 7x - 30 = (x - 10)(x + 3)$

Step 2: Find the critical points by setting the expression to zero and solving for $x$: $x - 10 = 0$ or $x + 3 = 0$

Solving for $x$ gives us: $x = 10$ or $x = -3$

Step 3: Determine the sign of the expression in the intervals created by the critical points: We'll create a number line and test the expression in three intervals: $(-∞, -3)$, $(-3, 10)$, and $(10, ∞)$.

Test $x = -4$ (choose any value less than -3): $(x - 10)(x + 3) = (-4 - 10)(-4 + 3) = (-14)(-1) = 14 > 0$

Test $x = 0$ (choose any value between -3 and 10): $(x - 10)(x + 3) = (0 - 10)(0 + 3) = (-10)(3) = -30 < 0$

Test $x = 11$ (choose any value greater than 10): $(x - 10)(x + 3) = (11 - 10)(11 + 3) = (1)(14) = 14 > 0$

Step 4: Identify the solution range for which the expression is greater than zero: From the tests above, we can see that the expression $(x - 10)(x + 3)$ is greater than zero in the intervals $(-∞, -3)$ and $(10, ∞)$. Therefore, the solution to the inequality is:

$x \in (-∞, -3) \cup (10, ∞)$

In interval notation, the solution is $(-∞, -3) \cup (10, ∞)$. This means any value of $x$ that falls within this range will satisfy the original inequality.