Question

A + b + c = 20 then prove that b + c square by 3 bc + c + a square by 300 + a + b square by 3 mb equals to 1

Answer 1

Plz write a correct and meaningful information .
I think Your question is -------> If a+b+c=0 ,then prove that (b+c)²/3bc + (c+a)²/3ac + (a+b)²/3ab =1 ?

LHS = (b + c)²/3bc + (c + a)²/3ac + (a + b)²/3ab
= a(b + c)²/3abc + b(c + a)²/3abc + c(a + b)²/3abc
= [a(b + c)² + b(c + a)² + c(a + b)² ]/3abc
= [b²a + c²a + 2abc + c²b + a²b + 2abc + a²c + b²c + 2abc ]/3abc
= [ab(b + a) + bc(c + b) + ca(a + c)+ 6abc]/3abc
∵ a + b + c = 0
a + b = -c
= [ab(-c) + bc(-a) + ca(-b) + 6abc]/3abc
= [-3abc + 6abc ]/3abc
= 3abc/3abc
= 1 = RHS