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

Step-by-step explanation:

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Answer 2

Answer:

Proved

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

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