if the lines ax + y + 1 = 0 , x + by + 1 =0 and x + y + c =0 where a,b and c are distinct real numbers different from 1 are constant concurrent , then the value of 1/ 1-a + 1/ 1-b + 1/ 1-c equals what?

ax+y+1=0....1orabx+by+b=0.....3x+by+1=0....4orax+aby+a=0....2Subtracting equation 1 and 2, 1-aby+1-a=0y = a-11-abSubtracting equation 3 and 4, ab-1x+b-1=0x = 1-bab-1Now if these three are concurrent so values of x and y will satisfy third equation, 1-bab-1+a-11-ab+c=0b-1+a-11-ab+c=0a+b-2+c-abc=0....5Now, 11-a+11-b+11-c=1-b-c+bc+1+ac-a-c+1+ab-a-b1-a1-b1-c=3-2a+b+c+ab+bc+ca1-a1+bc-b-c=3-22+abc+ab+bc+ca1+bc-b+c+a-abc+ab+ac Using equation 5=-1-2abc+ab+bc+ca1+bc-2+abc-abc+ab+ac=-1-2abc+ab+bc+ca-1-2abc+ab+bc+ca=1

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