Question

1)√11-5x=1-x 2)√2x-3=x-3 3)√3x+49=10 4)1/√x=1/8 5)√-9+9x-3=0 6)√6/4x-54=1/7 7)3^√x+6=4 8)5x-7/2=3

Answer 1

Ответ:

1) √11-5х = 1-х

-5х + х = 1 - √11

-4х = 1 - √11

х = - 1/4 + √11/4

х = -1 + √11 /4

х = 0,579156

Answer 2

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

1. √11 - 5x = 1 - x

Let's isolate the variable x:

-5x + x = 1 - √11

-4x = 1 - √11

x = (1 - √11) / -4

2. √2x - 3 = x - 3

Let's isolate the variable x:

√2x - x = 3 - 3

(√2 - 1)x = 0

x = 0 / (√2 - 1)

x = 0

3. √(3x + 49) = 10

Let's isolate the square root:

3x + 49 = 10^2

3x + 49 = 100

3x = 100 - 49

3x = 51

x = 51 / 3

x = 17

4. 1/√x = 1/8

Let's isolate the variable x:

√x = 8

x = 8^2

x = 64

5. √(-9) + 9x - 3 = 0

The square root of a negative number is undefined, so this equation has no real solutions.

6. √(6/4x - 54) = 1/7

Let's isolate the square root:

6/4x - 54 = (1/7)^2

6/4x - 54 = 1/49

6/4x = 1/49 + 54

6/4x = (1 + 49*54) / 49

x = 4 * (1 + 49*54) / (6 * 49)

7. 3^√(x + 6) = 4

Let's isolate the exponentiated term:

√(x + 6) = log₃(4)

x + 6 = 3^(log₃(4))

x + 6 = 4

x = 4 - 6

x = -2

8. 5x - 7/2 = 3

Let's isolate the variable x:

5x = 3 + 7/2

5x = (3*2 + 7) / 2

5x = (6 + 7) / 2

5x = 13 / 2

x = 13 / (2 * 5)

x = 13 / 10

Please note that for equation 5), there is no real solution since the square root of a negative number is undefined.