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

Step 1 ：$\sqrt{x-1\sqrt{2x-2}}=2$

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

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

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 ：$\boxed{{\displaystyle x=2,x=9}}$