Find the only possible triplet (a,b,c) of real numbers that satisfy this system of equations

• (a-1)(b-1)(c-1) = a*b*c - 1
• (a-2)(b-2)(c-2) = a*b*c - 2

Prove that no further triplet satisfy the given conditions.

**** Computer program/ excel solver assisted solutions are welcome, but a semi-analytic - namely, p&p and hand calculator based methodology is preferred.