Question

If a+b+c=0,then (a/bc)²+(b/ca)²+(c/ab)²=?​

Answer 1

Answer:

$\frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ac} + \frac{ {c}^{2} }{ab} = 3$

Step-by-step explanation:

$e = \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ac} + \frac{ {c}^{2} }{ab} = \\ \\ \\ \\ now \: \: \: {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ therefore \: \: \: {a }^{2} + {b}^{2} + {c}^{2} = - 2(ab + bc + ca) \\ \\ because \: \: \: a + b + c = 0 \\ therefore \: \: \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc \\ \\ now \: \: \: \: e = \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ac} + \frac{ {c}^{2} }{ab} \\ \\ e = \frac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc} \: \: \: using \: \: {a}^{3} + {b}^{3} + {c}^{3} = 3abc \\ \\ e = \frac{3abc}{abc} \\ \\ \\ e= 3$