If a, b, c are all non-zeros and a + b + c = 0, prove a^2/bc+b^2/ac+c^2/ab=3
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Answered by
8
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)
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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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Answered by
4
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
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