Question

Решить неравенство 4х^2-9>0 с помощью графика

Answer 1

Solving the Inequality 4x^2 - 9 > 0 Using a Graph

To solve the inequality 4x^2 - 9 > 0 using a graph, we need to find the values of x that satisfy the inequality. This can be done by graphing the quadratic function 4x^2 - 9 and identifying the regions where the graph is above the x-axis.

To graph the function, we can start by finding the x-intercepts, if any. The x-intercepts are the points where the graph intersects the x-axis. In this case, the function 4x^2 - 9 = 0 can be factored as (2x - 3)(2x + 3) = 0. Solving for x, we find that x = 3/2 or x = -3/2. These are the x-intercepts of the graph.

Next, we can determine the behavior of the graph by considering the leading coefficient, which is positive in this case (4 > 0). This means that the graph opens upwards, forming a "U" shape.

Since the leading coefficient is positive and the graph has x-intercepts, the graph will be above the x-axis in the regions between the x-intercepts. Therefore, the solution to the inequality 4x^2 - 9 > 0 is the set of x-values that lie between the x-intercepts.

To summarize: - The x-intercepts of the graph are x = 3/2 and x = -3/2. - The graph opens upwards. - The solution to the inequality 4x^2 - 9 > 0 is the set of x-values that lie between the x-intercepts.

Please note that without specific values for x, it is not possible to provide an exact range of x-values that satisfy the inequality. However, by graphing the function, you can visually determine the regions where the graph is above the x-axis, which represent the solution to the inequality.

I hope this helps! Let me know if you have any further questions.