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