Question

Let a, b and c be such that a + b + c = 0 and P =a^2/2a^2 + bc + b^2/2b^2 + ca + c^2/2c^2 + ab is defiend. What is the value of P?

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 =