Let's solve each equation one by one.

1) √x - 1 = x - 2
First, let's isolate the square root term on one side:
√x = x - 1 + 2
√x = x + 1

Now we square both sides:
x = (x + 1)^2
x = x^2 + 2x + 1

Rearranging the terms, we get a quadratic equation:
x^2 - x - 1 = 0

Using the quadratic formula:
x = [1 ± √(1 + 4)] / 2
x = [1 ± √5] / 2

So the solutions for this equation are x = (1 + √5) / 2 or x = (1 - √5) / 2.

2) √x + 2 = x
Let's isolate the square root term:
√x = x - 2
Square both sides:
x = (x - 2)^2
x = x^2 - 4x + 4

Rearranging the terms gives:
x^2 - 5x + 4 = 0

Using the quadratic formula:
x = [5 ± √(25 - 16)] / 2
x = [5 ± 3] / 2
x = 4 or x = 1

So the solutions for this equation are x = 4 or x = 1.

3) √2x - 4 = -3
Let's isolate the square root term:
√2x = -3 + 4
√2x = 1

Squaring both sides gives:
2x = 1
x = 1/2

So the solution for this equation is x = 1/2.

In summary:
x = (1 + √5) / 2 or x = (1 - √5) / 2 or x = 4 or x = 1 or x = 1/2.