Question

9х^2+1/х-4>0 Решите пожалуйста.

Answer 1

Ответ:

15 324578964

Пошаговое объяснение:

Answer 2

To solve the inequality $9x^2 + \frac{1}{x} - 4 > 0$, we need to find the intervals for $x$ that satisfy the inequality. Here's the step-by-step solution:

1. Get a common denominator for the terms in the expression: $9x^2 + \frac{1}{x} - 4 > 0$.

Multiplying the whole inequality by $x$ to get rid of the fraction: $9x^3 + 1 - 4x > 0$.

2. Now, let's find the critical points by setting the expression inside the inequality to zero:

$9x^3 + 1 - 4x = 0$.

3. Solve for $x$ by factoring or using numerical methods (e.g., Newton-Raphson method). In this case, let's factor it:

$9x^3 - 4x + 1 = 0$.

Unfortunately, this cubic equation does not have simple integer roots. To find the exact roots, you'll need to use numerical methods or a graphing calculator.

4. Once you find the critical points, they divide the number line into intervals. Choose a value from each interval and test it in the original inequality to determine whether it's part of the solution.

For example, let's assume $x = 0$:

$9(0)^2 + \frac{1}{0} - 4 = \text{undefined}$.

Since $x = 0$ leads to an undefined term in the original inequality, we should exclude it from the solution.

5. Test another value, say $x = 1$:

$9(1)^2 + \frac{1}{1} - 4 = 6 > 0$.

Now, we know that the interval containing $x = 1$ satisfies the inequality.

6. Test a value in the interval to the left of the critical point (e.g., $x = -1$):

$9(-1)^2 + \frac{1}{-1} - 4 = -12 < 0$.

This interval does not satisfy the inequality.

7. Test a value in the interval to the right of the critical point (e.g., $x = 2$):

$9(2)^2 + \frac{1}{2} - 4 = \frac{45}{2} > 0$.

This interval satisfies the inequality.

8. Therefore, the solution to the inequality $9x^2 + \frac{1}{x} - 4 > 0$ is:

$x \in (1, \text{root1}) \cup (\text{root2}, \text{root3})$,

where $1$ is the value we found to be satisfied, and $\text{root1}$, $\text{root2}$, and $\text{root3}$ are the real roots of the equation $9x^3 - 4x + 1 = 0$.