Question

(х-1)(х+2)больше доринюе 0

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the inequality $(x-1)(x+2) > 0$, we'll first find the critical points where the expression equals zero and then examine the sign of the expression in the intervals between those critical points.

Step 1: Find critical points: To find the critical points, set the expression equal to zero and solve for $x$:

$(x - 1)(x + 2) = 0$

Now, we have two critical points: $x - 1 = 0$ => $x = 1$ $x + 2 = 0$ => $x = -2$

Step 2: Determine the sign of the expression in each interval: Now, we have three intervals to consider: $(-\infty, -2)$, $(-2, 1)$, and $(1, \infty)$. We can choose any test point in each interval to determine the sign of the expression.

1. Test a point in $(- \infty, -2)$: Let's choose $x = -3$. $(x - 1)(x + 2) = (-3 - 1)(-3 + 2) = (-4)(-1) = 4 > 0$

2. Test a point in $(-2, 1)$: Let's choose $x = 0$. $(x - 1)(x + 2) = (0 - 1)(0 + 2) = (-1)(2) = -2 < 0$

3. Test a point in $(1, \infty)$: Let's choose $x = 2$. $(x - 1)(x + 2) = (2 - 1)(2 + 2) = (1)(4) = 4 > 0$

Step 3: Analyze the intervals: The expression $(x - 1)(x + 2)$ is greater than zero in the intervals $(- \infty, -2)$ and $(1, \infty)$ since it's positive in those intervals.

However, the expression is less than zero in the interval $(-2, 1)$ since it's negative in that interval.

Step 4: Final solution: To satisfy the inequality $(x - 1)(x + 2) > 0$, we need $x$ to be in either $(- \infty, -2)$ or $(1, \infty)$. Thus, the solution to the inequality is:

$x < -2 \text{ or } x > 1$