Question

1-х^2/х-0,2>0 дробь это деление

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the inequality (1 - x^2) / (x - 0.2) > 0, we need to find the intervals where the expression on the left-hand side is positive.

First, let's find the critical points by setting the numerator and denominator equal to zero:

Numerator: 1 - x^2 = 0 This can be factored as (1 - x)(1 + x) = 0, so the critical points are x = 1 and x = -1.

Denominator: x - 0.2 = 0 Solving for x, we get x = 0.2.

Now, we have three critical points: x = 1, x = -1, and x = 0.2.

Next, we'll test the intervals between these critical points to determine where the inequality is satisfied. We can pick test points from each interval and check the sign of the expression.

1. Interval: x < -1 Test point: Choose x = -2 (a value less than -1) (1 - (-2)^2) / (-2 - 0.2) = (1 - 4) / (-2.2) = -3 / (-2.2) ≈ 1.36 Since the expression is positive for x < -1, this interval is part of the solution.

2. Interval: -1 < x < 0.2 Test point: Choose x = 0 (a value between -1 and 0.2) (1 - 0^2) / (0 - 0.2) = 1 / (-0.2) ≈ -5 The expression is negative for x in this interval, so it is not part of the solution.

3. Interval: 0.2 < x < 1 Test point: Choose x = 0.5 (a value between 0.2 and 1) (1 - 0.5^2) / (0.5 - 0.2) = (1 - 0.25) / 0.3 ≈ 0.583 The expression is positive for x in this interval, so it is part of the solution.

4. Interval: x > 1 Test point: Choose x = 2 (a value greater than 1) (1 - 2^2) / (2 - 0.2) = (1 - 4) / 1.8 ≈ -1.67 The expression is negative for x > 1, so this interval is not part of the solution.

In conclusion, the solution to the inequality (1 - x^2) / (x - 0.2) > 0 is: x < -1 or 0.2 < x < 1.