If a+b+c=4 and a b+b c+c a=0 , then what is the value of the following determinant? | array lll a & b & c b & c & a c & a & b array |

Step-by-step solution

(a+b+c)=4 (Given) Now, | array lll a & b & c b & c & a c & a & b array |=a (b c-a^2 )+b (a c-b^2 )+c (a b-c^2 )=3 a b c-a^3-b^3-c^3 aligned & =- (a^3+b^3+c^3-3 a b c )=-(a+b+c)^3 & =-(4)^3=-64 . aligned