Question

2.15. При каком значении переменной x верно равенство: 1) √х= 11; 2) √х = 1,1; 3) √– х = 19;4) 2√x = 0,4; 5) 0,1√ х = 1; 6) √2х = -22?​

Answer 1

1)121

2)121/100

3)-361

4)1/25

5)100

6)нет решений

Answer 2

1. √x = 11

To find the value of x, we need to square both sides of the equation:

(√x)² = 11² x = 121

So, when x = 121, the equation √x = 11 is satisfied.

2. √x = 1.1

Squaring both sides:

(√x)² = (1.1)² x = 1.21

So, when x = 1.21, the equation √x = 1.1 is satisfied.

3. √(-x) = 19

This equation has no real solutions because the square root of a negative number is not defined in the real number system. So, there is no value of x that satisfies the equation √(-x) = 19.

4. 2√x = 0.4

Dividing both sides by 2:

√x = 0.4/2 √x = 0.2

Squaring both sides:

(√x)² = (0.2)² x = 0.04

So, when x = 0.04, the equation 2√x = 0.4 is satisfied.

5. 0.1√x = 1

Dividing both sides by 0.1:

√x = 1/0.1 √x = 10

Squaring both sides:

(√x)² = 10² x = 100

So, when x = 100, the equation 0.1√x = 1 is satisfied.

6. √(2x) = -22

This equation has no real solutions because the square root of a non-negative number is always non-negative. So, there is no value of x that satisfies the equation √(2x) = -22.