Answer :

Given:


Lines x + ay + a = 0, bx + y + b = 0 and cx + cy + 1 = 0


To find:


The value of 2abc – ab – bc – ca.


Explanation:


The given lines are


x + ay + a = 0 … (1)


bx + y + b = 0 … (2)


cx + cy + 1 = 0 … (3)


It is given that the lines (1), (2) and (3) are concurrent.



(1 – bc) – a(b – bc) + a(bc – c) = 0


1 – bc – ab + abc + abc – ac = 0


2abc – ab – bc – ca = -1


Hence, the value of 2abc ab bc ca is 1


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