Question

1. √x=-4 2. √x²=16 3. √x-4=0

Answer 1

1.В первом случаи уравнение не имеет решения, тк корень величина положительная (комплексные числа не рассматриваются)
2. корень квадратный из x² = |x|.
|x|=16
x=±16
3. Переносим - 4 в правую часть.
$\sqrt{x} = 4$
Возводим в квадрат
x=16

Answer 2

Ответ:

1. √х = - 4

х є ∅ , тк √х не может быть отрицательным числом.

Ответ: ∅

2. √х² = 16

| х | = 16 , тогда

х1 = 16

х2 = - 16

Ответ: -16 ; 16

3. √х - 4 = 0

√х = 4

х = 4²

х = 16

Ответ: 16

Answer 3

Let's solve each of the equations step by step:

1. √x = -4: To solve this equation, we square both sides to eliminate the square root: (√x)² = (-4)² x = 16

Therefore, the solution to the equation √x = -4 is x = 16.

2. √x² = 16: Here, we can simplify the left side by recognizing that the square root of a squared number is the absolute value of that number: |x| = 16

The absolute value of a number can be positive or negative, so we have two cases to consider:

Case 1: x = 16: In this case, the absolute value of 16 is 16. So x = 16 is a solution.

Case 2: x = -16: In this case, the absolute value of -16 is also 16. So x = -16 is another solution.

Therefore, the equation √x² = 16 has two solutions: x = 16 and x = -16.

3. √x - 4 = 0: To solve this equation, we isolate the square root term by adding 4 to both sides: √x = 4

Now, we square both sides to eliminate the square root: (√x)² = 4² x = 16

Therefore, the solution to the equation √x - 4 = 0 is x = 16.