Question

6x-x^2≥0 как разложить чтоб получились корни (разве не должно быть так: x(6+x)≤0 x=0 x=-6 ?(

Answer 1

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Answer 2

You are correct! The inequality can be simplified and factored as follows:

Starting with the inequality: 6x - x^2 ≥ 0

Step 1: Factor out an 'x' from both terms: x(6 - x) ≥ 0

Step 2: Now, we have two factors: x and (6 - x).

To find the solutions where the inequality holds true (x ≥ 0 or x ≤ 6), we need to analyze the sign of each factor separately.

Factor 1: x For x to be positive (x > 0), the inequality holds true.

Factor 2: (6 - x) For (6 - x) to be positive (6 - x > 0), x must be less than 6 (x < 6).

Now, let's summarize the conditions for the inequality to be true:

1. x ≥ 0 (Since the factor x must be positive or zero)
2. x < 6 (Since the factor (6 - x) must be positive)

Combining both conditions, we get the final solution:

0 ≤ x < 6

So, the values of x that satisfy the inequality are all real numbers between 0 (inclusive) and 6 (exclusive), i.e., x ∈ [0, 6).