If `a,b,c` are real numbers such that `3(a^(2)+b^(2)+c^(2)+1)=2(a+b+c+ab+bc+ca)`, than `a,b,c`are in

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

If a+b+ c =9 and a^(2) + b^(2) + c^(2) = 29 , find ab + bc + ca .

If a-b-c= 3 and a^(2) + b^(2) + c^(2) = 77 , find: ab- bc+ ca

If a + b- c = 4 and a^(2) + b^(2) + c^(2)= 38 , find ab- bc - ca

If a^(2) + b^(2) + c^(2) = 35 and ab+ bc + ca= 23 , find a + b+ c

If a^(2) + b^(2) + c^(2) = 50 and ab +bc + ca= 47 , find a + b+ c

If a, b, c are non zero complex numbers satisfying a^(2) + b^(2) + c^(2) = 0 and |(b^(2) + c^(2),ab,ac),(ab,c^(2) + a^(2),bc),(ac,bc,a^(2) + b^(2))| = k a^(2) b^(2) c^(2) , then k is equal to

If a+b+c = 10 and a^(2) + b^(2) + c^(2) = 38 , find : ab + bc + ca

If a+b+c =11 and a^(2) + b^(2) + c^(2) =81 , find : ab + bc + ca .