2006-II-06

Ans: B
I is not an identity. For $x=1$,

$\begin{array}{rcl}
\text{LS} & = & (1)^2 -4 \\
& = & -3 \\
\text{RS} & = & 0 \\
\therefore \text{LS} & \neq & \text{RS}
\end{array}$

II is not an identity. For $x=1$,

$\begin{array}{rcl}
\text{LS} & = & (1)^2 -4 \\
& = & -3 \\
\text{RS} & = & ((1)-2)^2 \\
& = & 1 \\
\therefore \text{LS} & \neq & \text{RS}
\end{array}$

III is an identity. For any values of $x$,

$\begin{array}{rcl}
\text{RS} & = & (x+2)(x-2) \\
& = & x^2 +2x -2x -4 \\
& = & x^2 -4 \\
\text{LS} & = & x^2 – 4 \\
\therefore \text{LS} & = & \text{RS}
\end{array}$