Question

-13/(x-3)в квадрате-4>или равно 0

Answer 1

Ответ:

25

Пошаговое объяснение:

уравнение

Answer 2

To solve the inequality $-\frac{{13}}{{(x-3)^2}} - 4 \geq 0$, we can follow these steps:

Step 1: Get rid of the fraction by multiplying both sides by $(x-3)^2$ (note that $(x-3)^2$ is always positive, so we don't need to worry about reversing the inequality when multiplying):

$-13 - 4(x-3)^2 \geq 0$

Step 2: Expand the square term:

$-13 - 4(x^2 - 6x + 9) \geq 0$

Step 3: Distribute the -4:

$-13 - 4x^2 + 24x - 36 \geq 0$

Step 4: Combine like terms:

$-4x^2 + 24x - 49 \geq 0$

Step 5: To solve this quadratic inequality, find the critical points by setting the expression equal to 0:

$-4x^2 + 24x - 49 = 0$

Step 6: Use the quadratic formula to find the critical points:

$x = \frac{{-b \pm \sqrt{{b^2-4ac}}}}{{2a}}$

For our quadratic $ax^2 + bx + c$, $a = -4$, $b = 24$, and $c = -49$.

$x = \frac{{-24 \pm \sqrt{{24^2 - 4 \cdot (-4) \cdot (-49)}}}}{{2 \cdot (-4)}}$

$x = \frac{{-24 \pm \sqrt{{576 - 784}}}}{{-8}}$

$x = \frac{{-24 \pm \sqrt{{-208}}}}{{-8}}$

Since the discriminant ($b^2 - 4ac$) is negative, the quadratic equation has no real solutions. Therefore, there are no critical points.

Step 7: Determine the concavity of the parabola:

Since the coefficient of $x^2$ is negative (-4), the parabola opens downwards.

Step 8: Analyze the sign of the inequality within different intervals:

Since the parabola opens downwards and has no real roots, it will be negative everywhere. Therefore, the solution to the inequality is all real values of $x$:

$-\frac{{13}}{{(x-3)^2}} - 4 \geq 0$ holds true for all real $x$.