b) $\sqrt{x-1 \sqrt{2 x-2}}=2$

Step 1 ：\(\sqrt{x-1 \sqrt{2 x-2}}=2\)

Step 2 ：Square both sides: \(x-1 \sqrt{2 x-2} = 2^2 = 4\)

Step 3 ：Move 4 to the left side: \(1 \sqrt{2 x-2} = x - 4\)

Step 4 ：Square both sides again: \(2x - 2 = (x - 4)^2\)

Step 5 ：Expand the right side: \(2x - 2 = x^2 - 8x + 16\)

Step 6 ：Move all terms to the right side: \(x^2 - 10x + 18 = 0\)

Step 7 ：Factor the quadratic: \((x - 2)(x - 9) = 0\)

Step 8 ：Solve for x: \(x = 2\) or \(x = 9\)

Step 9 ：Check the solutions: \(\sqrt{2-1 \sqrt{2 \cdot 2-2}}=2\) and \(\sqrt{9-1 \sqrt{2 \cdot 9-2}}=2\)

Step 10 ：\(\boxed{x = 2, x = 9}\)