If | array lll a & 1 & 1 1 & b & 1 1 & 1 & c array | 0 , then a b c

Step-by-step solution

Since, | array ccc a & 1 & 1 1 & b & 1 1 & 1 & c array | 0a(b c-1)-(c-1)+(1-b) 0 2+a b c a+b+c ....(i) Since, A . M . G . M . a+b+c 3(a b c)^ 1 / 3 ....(ii) aligned & By (i) and (ii), we get 2+a b c 3(a b c)^ 1 / 3 & 2+x^3 3 x ; [ Let, (a b c)^ 1 / 3 =x ] & (x-1) (x^2+x-2 ) 0 (x-1)^2(x+2) 0 & x -2 (a b c)^ 1 / 3 -2 (a b c) -8 aligned