Question

X2+6x-27 менше строге 0

Answer 1

Х1=-9
х2=3

___+___-9___-___3___+____
(-9;3)

Answer 2

To solve the inequality $x^2 + 6x - 27 < 0$, we need to find the values of $x$ that satisfy this inequality. One way to do this is by factoring the quadratic expression. The factored form of $x^2 + 6x - 27$ is $(x + 9)(x - 3)$.

Now, we want to find the values of $x$ for which $(x + 9)(x - 3) < 0$. To do that, we'll create a sign chart. A sign chart helps us determine the sign of the expression $(x + 9)(x - 3)$ for different intervals of $x$.

1. Find critical points: Set each factor equal to zero and solve for $x$: $x + 9 = 0$ => $x = -9$ $x - 3 = 0$ => $x = 3$

2. Create the sign chart:

   scssCopy code
    | (-∞) |  -9  |  (3)  |  ∞  |
   

   ---

   x + 9 | - | 0 | + | + | x - 3 | - | - | - | + |

   Product| + | 0 | - | + |

3. Interpretation: From the sign chart, we see that $(x + 9)(x - 3) < 0$ for the interval between -9 and 3 (not including -9 and 3). In interval notation, this is written as $-9 < x < 3$.

So, the solution to the inequality $x^2 + 6x - 27 < 0$ is $x \in (-9, 3)$.