Question

√х-1 >-4√х-1 >4 √х-1 <4 √х-1 <-4 Хелп

Answer 1

Ответ:

білмим қай пәннен сабақ

Answer 2

The inequalities you've written are as follows:

1. √x - 1 > -4
2. -4√x - 1 > 4
3. 4√x - 1 < 4
4. 4√x - 1 < -4

Let's solve each of them step by step:

1. √x - 1 > -4 Add 1 to both sides: √x > -3

2. -4√x - 1 > 4 Add 1 to both sides: -4√x > 5 Divide both sides by -4. When you divide by a negative number, flip the inequality sign: √x < -5/4

3. 4√x - 1 < 4 Add 1 to both sides: 4√x < 5 Divide both sides by 4: √x < 5/4

4. 4√x - 1 < -4 Add 1 to both sides: 4√x < -3 Divide both sides by 4: √x < -3/4

Now, to find the valid solution, we need to consider the domain of the square root function. The square root of a real number must be non-negative. Therefore, the valid solutions are:

1. √x > -3 (Since the square root is always non-negative, this is always true.)
2. No valid solutions, as the square root of a real number is always non-negative, and it can't be less than -5/4.
3. √x < 5/4 (This is valid within the domain of the square root.)
4. No valid solutions, as the square root of a real number is always non-negative, and it can't be less than -3/4.

So, the valid solution is: √x > -3 and √x < 5/4

However, keep in mind that this solution only applies to the range of x values for which the square root function is defined. In this case, x must be greater than or equal to 0 because the square root of a negative number is not a real number.