Question

3x²-4x+1<0решите неравенство​

Answer 1

Ответ:

Объяснение: решаем методом интервалов, на числовой прямой отметим нули  1 и 1/3, проставим знаки  в промежутках

   +                   -               +

           1/3                 1

ответ    х   ∈  (1/3;1)

Answer 2

To solve the inequality 3x² - 4x + 1 < 0, we can use a few different methods. One common approach is to factor the quadratic expression and then analyze the sign of each factor in the intervals they create. Another method is to use the quadratic formula. Let's go through both methods:

Method 1: Factoring Step 1: Factor the quadratic expression: 3x² - 4x + 1 = (3x - 1)(x - 1)

Step 2: Set each factor equal to zero and solve for x: 3x - 1 = 0 => 3x = 1 => x = 1/3 x - 1 = 0 => x = 1

Step 3: Use a sign chart to determine the intervals where the expression is less than zero:

sqlCopy code
     +---------+---------+---------+
     |         |    -    |    +    |
     +---------+---------+---------+
     | 3x - 1  |    -    |    +    |
     +---------+---------+---------+
     |   x - 1 |    -    |    +    |
     +---------+---------+---------+
     | Result  |    -    |    +    |
     +---------+---------+---------+

The solution to the inequality is 1/3 < x < 1.

Method 2: Quadratic Formula Step 1: Use the quadratic formula to find the solutions to the quadratic equation 3x² - 4x + 1 = 0: x = (-b ± √(b² - 4ac)) / 2a where a = 3, b = -4, and c = 1.

x = [4 ± √((-4)² - 4 * 3 * 1)] / 2 * 3 x = [4 ± √(16 - 12)] / 6 x = (4 ± √4) / 6 x = (4 ± 2) / 6

Step 2: Find the two solutions: x₁ = (4 + 2) / 6 = 6 / 6 = 1 x₂ = (4 - 2) / 6 = 2 / 6 = 1/3

Step 3: Use a sign chart to determine the intervals where the expression is less than zero, just like in method 1.

Since both methods agree, the solution to the inequality is 1/3 < x < 1.