Question

X²+4x+3 больше 0решите неравенство

Answer 1

$no numeric noise key 1026^no numeric noise key 1025 + 4x 3> 0 \\ (x + 1)(x + 3) > 0$
+ - +
————0————0———>
- 3 - 1
Ответ: (-00; - 3) U (-1; +00)

Answer 2

To solve the inequality $x^2 + 4x + 3 > 0$, we can use various methods. One common approach is to factor the quadratic expression or use the quadratic formula. Let's factor the expression first:

$x^2 + 4x + 3 > 0$

The expression can be factored as:

$(x + 3)(x + 1) > 0$

Now, we need to find the intervals where the expression $(x + 3)(x + 1)$ is greater than zero.

To do this, we can use a sign chart or test values from each interval:

1. For $x < -3$: Choose $x = -4$ (a value less than -3) $(-4 + 3)(-4 + 1) = (-1)(-3) = 3 > 0$

2. For $-3 < x < -1$: Choose $x = -2$ (a value between -3 and -1) $(-2 + 3)(-2 + 1) = (1)(-1) = -1 < 0$

3. For $x > -1$: Choose $x = 0$ (a value greater than -1) $(0 + 3)(0 + 1) = (3)(1) = 3 > 0$

The inequality is satisfied for $x < -3$ and $x > -1$. Therefore, the solution to the inequality $x^2 + 4x + 3 > 0$ is:

$x < -3$ or $x > -1$