Question

Решите уравнения 1) √x=0.2 2)7√x=14 3)√x+6=0 4)4-3√x=0

Answer 1

1) √x=0.2

(√х)^2=0,2^2

Х=0,04

2)7√x=14

√х=14:7

√х=2

(√х)^2=2^2

Х=4

3)√(x+6)=0

х+6=0

Х=-6

4)4-3√x=0

3√х=4

√х=4/3

(√х)^2=(4/3)^2

Х=16/9

Answer 2

1. √x = 0.2

To solve this equation, we need to isolate the square root term on one side of the equation. We can do this by squaring both sides of the equation:

(√x)^2 = (0.2)^2

x = 0.04

Therefore, the solution to the equation is x = 0.04.

2. 7√x = 14

To solve this equation, we need to isolate the square root term. We can do this by dividing both sides of the equation by 7:

(7√x)/7 = 14/7

√x = 2

To eliminate the square root, we square both sides of the equation:

(√x)^2 = 2^2

x = 4

Therefore, the solution to the equation is x = 4.

3. √x + 6 = 0

To solve this equation, we need to isolate the square root term. We can do this by subtracting 6 from both sides of the equation:

√x = -6

However, since the square root of a number is always non-negative, there is no real number solution to this equation. Therefore, this equation has no solution.

4. 4 - 3√x = 0

To solve this equation, we need to isolate the square root term. We can do this by subtracting 4 from both sides of the equation:

-3√x = -4

Next, we divide both sides of the equation by -3:

√x = 4/3

To eliminate the square root, we square both sides of the equation:

(√x)^2 = (4/3)^2

x = 16/9

Therefore, the solution to the equation is x = 16/9.