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

If `a , b , c` are non-zero real numbers and if the system of equations `(a-1)x=y=z` `(b-1)y=z+x` `(c-1)z=x+y` has a non-trivial solution, then prove that `a b+b c+c a=a b c`

a + b + c

abc

`-1`

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