Question

a^2+b^2+c^2+ab+bc+ca=0,prove that b+c=a?​

Answer 1

Answer:

$a ^ { 2 } + b ^ { 2 } + c ^ { 2 } + a b + b c + c a = 0$

also from question

$b ^ { 2 } + c ^ { 2 } + 2 b c = b c - a b - a c - a ^ { 2 }$

$( b + c ) ^ { 2 } = b c - a ( b + c + a )$

$a ( b + c + a ) + ( b + c ) ^ { 2 } - b c = 0$

This is a quadratic in a which will give two values if a in terms of b and c neither of which is b+c

so your question is wrong