Question

If a, b, c are all non-zeros and a + b + c = 0, prove a^2/bc+b^2/ac+c^2/ab=3

Answer 1

Answer:

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It is given that,

a+b+c=0 ----(1)

To prove:

a²/bc + b²/ac + c²/ab = 3

Explanation:

______________________

We know that,

if x+y+z = 0 then

x³+y³+z³ =3xyz ------(2)

______________________

LHS = a²/bc + b²/ac + c²/ab

= a³/abc + b³/abc + c³/abc

=( a³+b³+c³)/(abc)

= (3abc)/(abc) [ from (2)]

After cancellation, we get

= 3

Therefore,

If a+b+c=0 then

a²/bc + b²/ac + c²/ab = 3

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Answer 2

Step-by-step explanation:

If a b care all non zero and a+b+c=0 prove that

a2/bc+b2/ca+c2/ab=3

a?/bc + b?/ca + c/ab = 3

Multiplying by abc both sides

=> a + b3 + c3 = 3abc

=> (a+ b) 3ab(a+b) + c = 3abc

as we know that a +b+c=0

=> a+b=-C

=> -c) - 3abc) + b = 3abc

=> -c + 3abc + c 3abc

=> 3abc = 3abc

=> LHS = RHS