(b) $\sqrt{x-4}=x-4$

Step 1 ：Squaring both sides of the equation \(\sqrt{x - 4} = x - 4\), we get \(x - 4 = (x - 4)^2\).

Step 2 ：Expanding the right side of the equation, we get \(x - 4 = x^2 - 8x + 16\).

Step 3 ：Rearranging the equation, we get \(x^2 - 9x + 20 = 0\).

Step 4 ：Factoring the quadratic equation, we get \((x - 4)(x - 5) = 0\).

Step 5 ：Setting each factor equal to zero gives the solutions \(x = 4\) and \(x = 5\).

Step 6 ：However, substituting \(x = 4\) back into the original equation, we get \(\sqrt{4 - 4} = 4 - 4\), which simplifies to \(0 = 0\).

Step 7 ：Substituting \(x = 5\) back into the original equation, we get \(\sqrt{5 - 4} = 5 - 4\), which simplifies to \(1 = 1\).

Step 8 ：Therefore, the solution to the equation \(\sqrt{x - 4} = x - 4\) is \(\boxed{x = 4, 5}\).