If a, b and c are real numbers, and fig 1 Show that either a+b+c=0 or a=b=c

fig 1= 

Given: 

  

 

Here,   Either 

 ……….(i)

Or 

  

  [Expanding along first row]

 

 

 

 

 

 

 

  and  and  

  and  and  ……….(ii)

Therefore, from eq. (i) and (ii), either  or