Question

$△=\left|\begin{array}{ccc}1+a^2+a^4& 1+ab+a^2{b}^2& 1+ac+a^2{c}^2\\ 1+ab+a^2{b}^2& 1+b^2+b^4& 1+bc+b^2{c}^2\\ 1+ac+a^2{c}^2& 1+bc+b^2{c}^2& 1+c^2+c^4\end{array}\right|$

• A. $(a-b{)}^2(b-c{)}^2(c-a{)}^2$
• B. $2(a-b)(b-c)(c-a)$
• C. $4(a-b)(b-c)(c-a)$
• D. None of these

Answer 1

Answer: (D)

None of these

$△=\left|\begin{array}{ccc}1+a^2+a^4& 1+ab+a^2{b}^2& 1+ac+a^2{c}^2\\ 1+ab+a^2{b}^2& 1+b^2+b^4& 1+bc+b^2{c}^2\\ 1+ac+a^2{c}^2& 1+bc+b^2{c}^2& 1+c^2+c^4\end{array}\right|$

Put $\Rightarrow a=1;b=2;c=3$

$△=\left|\begin{array}{ccc}3& 7& 1\\ 7& 3& 3\\ 1& 3& 3\end{array}\right|$

$△=(9-9)-7(21-3)+1(21-3)$

$=0-7\left(18\right)+18$

$=18(-7+1)$

$=18(-6)$

$△=-108$

$\therefore$ None of these.