If \( x, y, z \in R \), then the value of determinant
\[
\left|\begin{array}{lll}
\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\
\left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\
\left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1
\end{array}\right| \text { is }
\]

Given that, \( \left|\begin{array}{ccc}\left(5^{x}+5^{-x}\right)^{2} & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ \left(6^{x}+6^{-x}\right)^{2} & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ \left(7^{x}+7^{-x}\right)^{2} & \left(7^{x}-7^{-x}\right)^{2} & 1\end{array}\right| \)
\( C_{1} \rightarrow C_{1}-C_{2} \)
\( \left|\begin{array}{ccc}4 & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ 4 & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ 4 & \left(7^{x}-7^{-x}\right)^{2} & 1\end{array}\right|=4\left|\begin{array}{ccc}1 & \left(5^{x}-5^{-x}\right)^{2} & 1 \\ 1 & \left(6^{x}-6^{-x}\right)^{2} & 1 \\ 1 & \left(7^{x}-7^{-x}\right)^{2} & 1\end{array}\right|=0 \)