\((\textbf{a})\) Given that \(|t|=3\), find the possible values of \(|2t-1|\).

\((\textbf{b})\) Solve the inequality \(|x-\sqrt2|>|x+3\sqrt2|\).

**Let the two possible values of \(|2t-1|\) be \(y\) and \(z\), and let \(x_{min}\) be the minimum value that \(x\) does not satisfy.**

**Input \(x_{min}^2+y+z\) as your answer.**

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