[a+b+c!=0],[[[a,b,9],[b,a,b]]=0quad " prove that "a=b]

If a+b+c!= and |(a,b,c),(b,c,a),(c,a,b)|=0 then prove that a=b=c

If a+b+c!= and |(a,b,c),(b,c,a),(c,a,b)|=0 then prove that a=b=c

If a+b+c ne 0 and |{:(a,b,c),(b,c,a),(c,a,b):}|=0 then prove that a=b=c

If abs((a,b,a-b),(b,c,b-c),(2,1,0))=0 , then prove that a,b,c are in GP.

If a+b+c!=0 and |a b c b c a c a b|=0 , then prove that a=b=cdot

If a+b+c!=0 and |a b c b c a c a b|=0 , then prove that a=b=cdot

If : a^2+b^2+c^2-a b-b c-c a=0 , prove that a=b=c

If |(a,b,aalpha+b),(b,c,balpha+c),(aalpha+b,balpha+c,0)|=0, prove that a,b,c, are in G.P. or alpha is a root of ax^(2)+ 2bx+c=0

If (a+b-c)/(a+ b) =(b+c-a)/(b+c) = (c+a-b)/(c+a) and a+b+cne 0, then prove that a = b = c.

If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{vmatrix} =0 then prove that a=b=c