If (a-b)(b-c)(c-a)=2 and a b c=6 , then what is the value of | array ccc a & b & c a^2 & b^2 & c^2 a^3 & b^3 & c^3 array | ?

Step-by-step solution

Let = | array ccc a & b & c a^2 & b^2 & c^2 a^3 & b^3 & c^3 array | aligned & =a b c | array ccc 1 & 1 & 1 a & b & c a^2 & b^2 & c^2 array | & =a b c | array ccc c₁ c₁-c₂ & and c₂ c₂-c₃ a-b & 0 & 1 (a-b)(a+b) & (b-c)(b+c) & c^2 array | & =a b c(a-b)(b-c) | array ccc 0 & 0 & 1 1 & 1 & c a+b & (b+c) & c^2 array | aligned aligned & =a b c(a-b)(b-c)(c-a) & =6 2=12 aligned