√x-1=x-2 √x+2=x √2x-4=-3

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Let's solve each equation one by one.

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

Now we square both sides
x = (x + 1)^
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)] /
x = [1 ± √5] / 2

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

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

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

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

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

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

Squaring both sides gives
2x =
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.