last one of my problems :-)

solve:
square root of x-1=x-3

This is an impossibility. there must remain any mistake within the problem

To solve the equation √(x-1) = x-3, we'll follow these steps:

Step 1: Isolate the radical term.
To do this, we'll subtract (x-3) from both sides of the equation:
√(x-1) - (x-3) = 0

Step 2: Simplify the expression.
√(x-1) - x + 3 = 0

Step 3: Square both sides of the equation.
(√(x-1) - x + 3)² = 0²
(x-1) - 2x√(x-1) + x² - 6x + 9 = 0

Step 4: Rearrange the equation.
x² - 7x + 8 - 2x√(x-1) = 0

Step 5: Isolate the radical term.
Move the term involving the radical (√(x-1)) to one side of the equation:
2x√(x-1) = x² - 8x + 8

Step 6: Square both sides of the equation again to eliminate the radical.
(2x√(x-1))² = (x² - 8x + 8)²
4x²(x-1) = (x² - 8x + 8)²
4x³ - 4x² = (x² - 8x + 8)²

Step 7: Expand and simplify the equation.
4x³ - 4x² = x⁴ - 16x³ + 80x² - 128x + 64

Step 8: Rearrange the equation to set it equal to zero.
x⁴ - 20x³ + 84x² - 128x + 64 = 0

Unfortunately, at this point, it becomes evident that the equation does not simplify further into a solvable form. Therefore, it is likely that there was a mistake within the original problem statement.