Question

1) Решите неравенство?
2х²-13х+6<0

Answer 1

Пошаговое объяснение:

To solve the inequality \(2x^2 - 13x + 6 < 0\), you can follow these steps:

1. Find the roots of the corresponding equation \(2x^2 - 13x + 6 = 0\). You can factor the quadratic equation or use the quadratic formula. The roots are \(x = 2\) and \(x = \frac{3}{2}\).

2. Plot these roots on the number line.

3. Test intervals between the roots and outside the roots with a test point to determine where the inequality holds true.

In this case, the roots are \(x = 2\) and \(x = \frac{3}{2}\). Now, test the intervals:

- Choose a test point less than \(\frac{3}{2}\), say \(x = 1\). Substituting this into the inequality, you get \(2(1)^2 - 13(1) + 6 = -5 < 0\), which is true.

- Choose a test point between \(\frac{3}{2}\) and 2, say \(x = 1.5\). Substituting this into the inequality, you get \(2(1.5)^2 - 13(1.5) + 6 = -0.25 < 0\), which is true.

- Choose a test point greater than 2, say \(x = 3\). Substituting this into the inequality, you get \(2(3)^2 - 13(3) + 6 = 3 > 0\), which is false.

So, the solution to the inequality \(2x^2 - 13x + 6 < 0\) is \(x \in \left(\frac{3}{2}, 2\right)\).