Question

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

Answer 1

$= \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ca} + \frac{ {c}^{2} }{ab} \\ = \frac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc} \\ = \frac{( {a + b + c)}^{3} + 3abc }{abc} \\ = \frac{0 + 3abc}{abc} \\ = \frac{3abc}{abc} \\ = 3$

Answer 2

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