| , * 20 c a^2 & b^2 & c^2 (a + 1) ^2 & (b + 1) ^2 & (c + 1) ^2 (… - Vidyadip

MCQ

$\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\{{{(a + 1)}^2}}&{{{(b + 1)}^2}}&{{{(c + 1)}^2}}\\{{{(a - 1)}^2}}&{{{(b - 1)}^2}}&{{{(c - 1)}^2}}\end{array}\,} \right| = $

✓
$4\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\1&1&1\end{array}\,} \right|$
B
$3\,\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\1&1&1\end{array}\,} \right|$
C
$2\,\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\1&1&1\end{array}\,} \right|$
D
None of these

✓

Answer

Correct option: A.

$4\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\1&1&1\end{array}\,} \right|$

a
(a) Apply ${R_2} - {R_3}$ and note that ${(x + y)^2} - {(x - y)^2} = 4xy$

$\therefore $ $\Delta = 4\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\{{{(a - 1)}^2}}&{{{(b - 1)}^2}}&{{{(c - 1)}^2}}\end{array}\,} \right|$

= $4\,\left| {\,\begin{array}{*{20}{c}}{{a^2}}&{{b^2}}&{{c^2}}\\a&b&c\\1&1&1\end{array}\,} \right|$

{Applying ${R_3} - ({R_1} - 2{R_2}) $}

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