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If a,b and c are non-zero real numbers a...

If a,b and c are non-zero real numbers and if the equation (a-1)x=y+z,(b-1)y=z+x,
(c-1)z=x+y has a non-trival solution then ab+bc+ca equals to

A

a+b+c

B

abc

C

1

D

None of these

Text Solution

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The correct Answer is:
B
For nontrivial solution
`|(a-1,-1,-1),(1,1-b,1),(1,1,1-c)|=0`
Applying `C_1 to C_1 -C_3` and `C_2 to C_2 -C_3` , then
`|(a,0,-1),(0,-b,1),(c,c,1-c)|=0 rArr ` a(-b+bc-c)-0+c(0-b)=0 `rArr` ab+bc+ca=abc
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