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Let a, b, c ne three distinct non-zero r...

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` , `(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`

Text Solution

Verified by Experts

The correct Answer is:
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`
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