Question

If a+ b+ c=0 then prove that bc/(2a^2 + bc) + ca/(2b^2 + ca) + ab/(2c^2 + ab) = 1

Answer 1

Answer:

Explanation:

As a+b+c=0, a=−(b+c) or a2=b2+c2+2bc

and 2a2+bc=a2+a2+bc

= a2+a(−b−c)+bc

=a(a−b)−c(a−b)

= (a−c)(a−b)

and similarly 2b+ca)=(b−c)(b−a) and 2c2+ab=(c−a)(c−b)

Hence 12a2+bc+12b2+ca+12c2+ab

= 1(a−c)(a−b)+1