Question

If a × b = b × c = c × a , show that a + b + c = 0.

Answer 1

Step-by-step explanation:

a×b = b×c

a = c

b×c = c×a

b=a

therefore

a=b=c

This case is only possible if

a = b=c = 1

or

a = b=c = 0

for second case=>

a +b +c = 0

Answer 2

Step-by-step explanation:

:a x b =b x c=c x a

:ab=bc=ca

:a-a=b-b=c-c

:0=0=0

:hence it is proved,a + b+ c=0