If a , b , c are real numbers satisfying | ( a 2 + 1 ) 2 ( a b + 1 ) 2 ( a c + 1 ) 2 ( a b + 1 ) 2 ( b 2 + 1 ) 2 ( b c + 1 ) 2 ( a c + 1 ) 2 ( b c + 1 ) 2 ( c 2 + 1 ) 2 | = k ( a - b ) 2 ( b - c ) 2 ( c - a ) 2 then k =

Question

$If a, b, c are real numbers satisfying$ $| \begin{matrix} {(a^{2} + 1)}^{2} & {(a b + 1)}^{2} & {(a c + 1)}^{2} \\ {(a b + 1)}^{2} & {(b^{2} + 1)}^{2} & {(b c + 1)}^{2} \\ {(a c + 1)}^{2} & {(b c + 1)}^{2} & {(c^{2} + 1)}^{2} \end{matrix} |$ $= k {(a - b)}^{2} {(b - c)}^{2} {(c - a)}^{2} then k =$

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(3)

$| \begin{matrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{matrix} |$ $| \begin{matrix} 1 & 1 & 1 \\ 2 a & 2 b & 2 c \\ a^{2} & b^{2} & c^{2} \end{matrix} |$

Solution

1 0

2 1

3 2

4 4

Ans.
(3)

$| \begin{matrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{matrix} |$ $| \begin{matrix} 1 & 1 & 1 \\ 2 a & 2 b & 2 c \\ a^{2} & b^{2} & c^{2} \end{matrix} |$

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Solution

Q. If a,b,c are real numbers satisfying |(a2+1)2(ab+1)2(ac+1)2(ab+1)2(b2+1)2(bc+1)2(ac+1)2(bc+1)2(c2+1)2|=k(a-b)2(b-c)2(c-a)2 then k=

1 0

2 1

3 2

4 4

Ans. (3) |1aa21bb21cc2| |1112a2b2ca2b2c2|

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Ans.
(3)

$| \begin{matrix} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{matrix} |$ $| \begin{matrix} 1 & 1 & 1 \\ 2 a & 2 b & 2 c \\ a^{2} & b^{2} & c^{2} \end{matrix} |$