Mark the tick against the correct answer in the following:
If a, b, c be distinct positive real numbers then the value of 
is
To find: Nature of 
We have, 
Applying 
⇒ 
Taking (a+b+c) common from R1
⇒ 
Expanding along R1
⇒ (a+b+c)[1{(b)(c)-(a)(a)} – 1{(b)(b)-(c)(a)} + 1{(a)(b)-(c)(c)}]
⇒ (a+b+c)[1{bc-a2} – 1{b2-ca} + 1{ba - c2}]
⇒ (a+b+c)[bc - a2 –b2 + ca + ab - c2]
⇒ -(a+b+c)[ c2 + a2 + b2 - ca - bc – ba ]
⇒ 
⇒ 
⇒ 
⇒ 
Clearly, we can see that the answer is negative
1