Question

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

Answer 1

a+c+b=0=>

a= - b-c=>

ca= - bc-c2=>

2b2+ca= b2-c2+b2-bc= - (b-c)(a-b)

lly, 2a2+bc= - (a-b)(c-a)

and 2c2+ab= - (c-a)(b-c)

Now, LHS = - a2/(a-b)(c-a) - b2/(b-c)(a-b) - c2/(c-a)(b-c)

now by LCM and multiplication

= - [a2b-a2c+b2c-ab2+ac2-bc2/ - (a2b-a2c+b2c-ab2+ac2-bc2)]= 1

= RHS (Proved)