Question

2x²-3x+1>=0 решите неравенство​

Answer 1

Объяснение:

возможно я не прав, но вроде бы вот так

Answer 2

To solve the inequality 2x² - 3x + 1 ≥ 0, we can use several methods. One approach is to factorize the quadratic expression and analyze the sign of each factor. Here's how you can do it:

Step 1: Factorize the quadratic expression if possible. The quadratic expression 2x² - 3x + 1 cannot be easily factorized. So, we'll use an alternative method.

Step 2: Find the roots of the quadratic equation. To find the roots of the quadratic equation 2x² - 3x + 1 = 0, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a).

In this case, a = 2, b = -3, and c = 1. Substituting these values into the quadratic formula, we have: x = (-(-3) ± √((-3)² - 4(2)(1))) / (2(2)) = (3 ± √(9 - 8)) / 4 = (3 ± √1) / 4 = (3 ± 1) / 4.

So the roots of the quadratic equation are x = 1 and x = 1/2.

Step 3: Analyze the sign of the expression. To determine the sign of 2x² - 3x + 1, we'll create a sign chart or use test points.

Test a value less than 1/2, for example, x = 0: 2(0)² - 3(0) + 1 = 1. Since the value is positive, the expression is positive in this interval.

Test a value between 1/2 and 1, for example, x = 3/4: 2(3/4)² - 3(3/4) + 1 = 1/16. Since the value is positive, the expression is positive in this interval.

Test a value greater than 1, for example, x = 2: 2(2)² - 3(2) + 1 = 3. Since the value is positive, the expression is positive in this interval.

Step 4: Write the solution. From the analysis above, we can see that the expression 2x² - 3x + 1 is positive for all x values less than 1/2 and greater than 1. So the solution to the inequality 2x² - 3x + 1 ≥ 0 is:

x ∈ (-∞, 1/2] ∪ (1, +∞).