Find the non-zero positive value of x which satisfies the equation \(\begin{vmatrix} x & 1 & 0 \\ 1 & x & 1 \\ 0 & 1 & x\end{vmatrix}\) = 0
x(x\(^2\) - 1) - x = 0
= x\(^3\) - 2x = 0
x(x\(^2\) - 2) = 0
x\(^2\) - 2 = 0
x\(^2\) = 2
x = \(\sqrt{2}\)
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