Question

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

Answer 1

Step-by-step explanation:

a+b+c=0

so, a3 + b3 + c3 =3abc

now,a2/bc +b2/ac +c2/ab=a3+ b3+ c3/abc

=3abc/abc

=3

Answer 2

≡QUESTION≡

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

                                                       

║⊕ANSWER⊕║

GIVEN

a, b, c are non - zero integers

a + b + c = 0

To Prove :- a²/bc  + b²/ca  + c²/ab = 3

We know that if a+b+c =0 ,

then a³ + b³ + c³ = 3abc

 

Now, we have:

LHS = a²/bc+b²/ca+c²/ab

= a³+b³+c³/abc

= 3 abc/abc

= 3

= RHS

Hence, proved