If a, b, c are sides of a scalene triangle, then the value of | array lll a & b & c b & c & a c & a & b array | is :

Step-by-step solution

aligned & | array lll a & b & c b & c & a c & a & b array |= | array ccc a+b+c & a+b+c & a+b+c b & c & a c & a & b array | &=(a+b+c) | array lll 1 & 1 & 1 b & c & a c & a & b array | &=(a+b+c) | array ccc 0 & 0 & 1 b-c & c-a & a c-a & a-b & b array | &=(a+b+c) [a b+b c+c a-a^2-b^2-c^2 ] &=-(a+b+c) [(a-b)^2+(b-c)^2+(c-a)^2 ] aligned Since a, b, c are sides of a scalene triangle, therefore at least two of the a, b, c will be unequal. array ll & (a-b)^2+(b-c)^2+(c-a)^2>0 & Also a+b+c>0 & -(a+b+c) [(a-b)^2+ . & .(b-c)^