If a, b and c are real numbers, and `Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0`. Show that either `a+b+c=0` or `a=b=c`

If a, b and c are real numbers, and triangle = |[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]| = 0 Show that either a+b+c = 0 or a=b=c

If a, b and c are real numbers , and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}| Show that either a+b+c=0 or a=b=c

If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) ]:}=0 Show that either a+b+c=0 "or" a= b= c .

If a,b and c are real numbers, and Delta ={:[( b+c,C+a,a+b),( c+a,a+b,b+c),( a+b,b+c,c+a) ]:}=0 Show that either a+b+c=0 "or" a= b= c .

Let a,b and c are real number and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0

If a,b,c are real numbers and abs[[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]]=0 ,show that a=b=c

If a, b and c are real numbers, and Delta=|b+cc+a a+b c+a a+bb+c a+bb+cc+a|=0 .Show that either a" "+" "b" "+" "c" "=" "0" "or" "a" "=" "b" "=" "c .

If a ,\ b ,\ c are real numbers such that |(b+c,c+a ,a+b),( c+a,a+b,b+c),(a+b,b+c,c+a)|=0 , then show that either a+b+c=0 or, a=b=c .

If a, b, c, are real numbers such that |{:(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a):}|=0, then show that either a+b+c=0 or, a=b=c.