Question

{х2-4х-12<0\х2-6х-7<0​

Answer 1

Ответ:

$\left\{\begin{array}{l}x^2-4x-12$

Answer 2

To solve the inequalities $x^2 - 4x - 12 < 0$ and $x^2 - 6x - 7 < 0$, you can use the method of factoring and the concept of sign charts.

1. $x^2 - 4x - 12 < 0$:

First, factor the quadratic equation:

$x^2 - 4x - 12 = (x - 6)(x + 2)$.

Now, create a sign chart for this inequality. We're looking for the values of $x$ that make the expression on the left side less than zero (i.e., negative).

luaCopy code
   -2      6
   |-------|-------|
   +       -       +

The sign chart shows that the inequality is satisfied when $-2 < x < 6$. Therefore, the solution to $x^2 - 4x - 12 < 0$ is $-2 < x < 6$.

2. $x^2 - 6x - 7 < 0$:

First, factor the quadratic equation:

$x^2 - 6x - 7 = (x - 7)(x + 1)$.

Now, create a sign chart for this inequality:

luaCopy code
   -1      7
   |-------|-------|
   +       -       +

The sign chart shows that the inequality is satisfied when $-1 < x < 7$. Therefore, the solution to $x^2 - 6x - 7 < 0$ is $-1 < x < 7$.

So, the solutions for the inequalities are:

1. $x^2 - 4x - 12 < 0$ is satisfied when $-2 < x < 6$.
2. $x^2 - 6x - 7 < 0$ is satisfied when $-1 < x < 7$.