Question

Решить уравнение: 1) √х+1=3 2) √х-2=5 3) √4+х=√2х-1

Answer 1

1)√x+1=3
√x=2
x=4
2)√x-2=5
√x=7
x=49

Answer 2

1. √(x + 1) = 3

To solve this equation, we need to isolate the square root term by squaring both sides of the equation:

(√(x + 1))^2 = 3^2

x + 1 = 9

Now, subtract 1 from both sides of the equation:

x = 9 - 1

x = 8

Therefore, the solution to the equation is x = 8.

2. √(x - 2) = 5

Similar to the previous equation, we'll isolate the square root term by squaring both sides:

(√(x - 2))^2 = 5^2

x - 2 = 25

Now, add 2 to both sides of the equation:

x = 25 + 2

x = 27

Thus, the solution to the equation is x = 27.

3. √(4 + x) = √(2x - 1)

To solve this equation, we'll square both sides to eliminate the square root:

(√(4 + x))^2 = (√(2x - 1))^2

4 + x = 2x - 1

Now, subtract x from both sides:

4 = x - 1

Add 1 to both sides:

5 = x

Hence, the solution to the equation is x = 5.