Question
Without expanding determinants, prove that
(ii) $\left|\begin{array}{lll}1 & y z & y+z \\ 1 & z x & z+x \\ 1 & x y & x+y\end{array}\right|=\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|$
(ii) $\left|\begin{array}{lll}1 & y z & y+z \\ 1 & z x & z+x \\ 1 & x y & x+y\end{array}\right|=\left|\begin{array}{lll}1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2\end{array}\right|$
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(iii) (0, 5), (0, -5), (5, 0)
$\lim _{x \rightarrow 0}\left[\frac{(25)^x-2(5)^x+1}{x^2}\right]$