Question

If a,b,c are all non-zero and a+b+c=0.prove that (a^2/bc)+(b^2/ca)+(c^2/ab)=3

Answer 1

Answer:

a²/bc  + b²/ca  + c²/ab = 3

Step-by-step explanation:

If a b c are all non zero and a+b+c=0 prove that a2/bc+b2/ca+c2/ab=3

a²/bc  + b²/ca  + c²/ab = 3

Multiplying by abc both sides

=> a³  + b³ + c³  = 3abc

=> (a+ b)³ - 3ab(a+b)  + c³  = 3abc

as we know that a + b + c = 0

=> a + b = -c

=> (-c)³ - 3ab(-c) + c³ = 3abc

=> -c³ + 3abc + c³ = 3abc

=> 3abc = 3abc

=> LHS = RHS

QED  

Proved