Question

Let `a`, `b`, `c` ne three distinct non-zero real numbers satisfying the system of equation `(1)/(a)+(1)/(a-1)+(1)/(a-2)=1` , `(b)+(1)/(b-1)+(1)/(b-2)=1` , `(1)/(c )+(1)/(c-1)+(1)/(c-2)=1`. Then `abc=`
A. `1`
B. `2`
C. `3`
D. `4`

Answer 1

Correct Answer - B
`(b)` `a`, `b`, `c` are roots of equation `(1)/(x)+(1)/(x-1)+(1)/(x-2)=1`
`implies(x-1)(x-2)+x(x-2)+x(x-1)=x(x-1)(x-2)`
`impliesx^(3)-6x^(2)+8x-2=0`