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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