a: \(\left|1-x\right|=\sqrt{2}-0,\left(1\right)\)
=>\(\left|x-1\right|=\sqrt{2}-\dfrac{1}{9}=\dfrac{9\sqrt{2}-1}{9}\)
=>\(\left[{}\begin{matrix}x-1=\dfrac{9\sqrt{2}-1}{9}\\x-1=\dfrac{-9\sqrt{2}+1}{9}\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=\dfrac{9\sqrt{2}-1}{9}+1=\dfrac{9\sqrt{2}+8}{9}\\x=\dfrac{-9\sqrt{2}+1}{9}+1=\dfrac{-9\sqrt{2}+10}{9}\end{matrix}\right.\)
b: \(\left|x-\sqrt{2}\right|=1,\left(4\right)\)
=>\(\left|x-\sqrt{2}\right|=\dfrac{13}{9}\)
=>\(\left[{}\begin{matrix}x-\sqrt{2}=\dfrac{13}{9}\\x-\sqrt{2}=-\dfrac{13}{9}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}+\dfrac{13}{9}=\dfrac{9\sqrt{2}+13}{9}\\x=-\dfrac{13}{9}+\sqrt{2}=\dfrac{-13+9\sqrt{2}}{9}\end{matrix}\right.\)
