If a+b+c = 0 , then find the value of a²/bc + b²/ca + c²/ab.
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Given Equation is a + b + c = 0
Then a + b = -c ----- (1)
Cubing on both sides, we get
(a + b)^3 = (-c)^3
a^3 + b^3 + 3ab(a + b) = (-c)^3
a^3 + b^3 + 3(-c) = (-c)^3
a^3 + b^3 + c^3 = 3abc
(a^3 + b^3 + c^3)/abc = 3
a^3/abc + b^3/abc + c^3/abc = 3
a^2/bc + b^2/ac + c^2/ab = 3
Therefore the value = 3.
Hope this helps!
Then a + b = -c ----- (1)
Cubing on both sides, we get
(a + b)^3 = (-c)^3
a^3 + b^3 + 3ab(a + b) = (-c)^3
a^3 + b^3 + 3(-c) = (-c)^3
a^3 + b^3 + c^3 = 3abc
(a^3 + b^3 + c^3)/abc = 3
a^3/abc + b^3/abc + c^3/abc = 3
a^2/bc + b^2/ac + c^2/ab = 3
Therefore the value = 3.
Hope this helps!
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