Question

If a+b+c=0 then show that a
$a$
​

Answer 1

If

a

+

b

+

c

=

0

Then,

a

=

−

b

−

c

=

−

(

b

+

c

)

Therefore,

a

2

−

b

c

=

(

−

(

b

+

c

)

)

2

−

b

c

=

(

b

+

c

)

2

−

b

c

=

b

2

+

c

2

+

2

b

c

−

b

c

=

b

2

+

c

2

+

b

c

b

2

−

c

a

=

b

2

−

c

(

−

(

b

+

c

)

)

=

b

2

+

c

2

+

b

c

c

2

−

a

b

=

c

2

−

(

−

(

b

+

c

)

b

)

=

c

2

+

b

2

+

b

c

So,

a

2

−

b

c

=

b

2

−

c

a

=

c

2

−

a

b

Q

E

D