Question

If a+b+c=0, then find the value of
(b+c)² + (c+a)² + (a+b)²
____ ___ ___
bc ca ab

Answer 1

a+b+c=0

a+b=  ( ⁻ c.) …………….(1)

( a + b)³ = (⁻c)³

a³ + b³ + 3ab(a+b) = ⁻c³

a³ + b³ +c³ + 3a.b(⁻c)=0

a³ + b³ + c³ = 3abc

Divide both side by abc

a²/bc  +  b²/ca   +  c²/ab   =  3