√x^2 -4x+5 = √x -1

To solve this equation, we can start by isolating one of the square roots on one side of the equation:

√x^2 -4x+5 - √x +1 = 0

Next, we can square both sides of the equation to eliminate the remaining square root:

(x^2 -4x+5) - 2√x^2 -4x+5)(√x -1) + (x-2√x+1) = 0

Simplifying this expression, we get:

x^2 -4x+5 - 2√x^3 -6x^2 +3x + 10√x -5√x^2 +1 = 0

Now, we can isolate the remaining square root on one side of the equation and square both sides again:

(x^2 -4x+5 -1)^2 = (2√x^3 -6x^2 +3x + 10√x -5√x^2)^2

Simplifying this expression, we get:

x^4 -8x^3 +26x^2 -36x +25 = 0

This equation can be solved using various methods, such as factoring or the quadratic formula. However, the solutions are not real numbers, so there is no real solution to the original equation.