Question

If a+b+c=0 prove
(b+c)(b-c)+a(a+2b)=o






9

Answer 1

(b+c)(b-c) + a(a+2b)
b^2-c^2+a^2+2ab
(a+b)^2-c^2
c^2-c^2
0

Answer 2

(b+c)(b-c)+a(a+2b)
b^2-c^2+a^2+2ab
a^2+b^2+2ab=(a+b)^2
so
(a+b)^2-c^2...........1
(a+b)=-c
squaring both side
(a+b)^2=-c^2............2
putting 2 in 1
c^2-c^2=0
hence proved



































(b+c)(b-c)+a(a+2b)
b^2-c^2+a^2+2ab
a^2+b^2+2ab=(a+b)^2
so
(a+b)^2-c^2...........1
(a+b)=-c
squaring both side
(a+b)^2=-c^2............2
putting 2 in 1
c^2-c^2=0
hence proved