Question

If a, b and c are all non zero and a+b+c=0.find the value of, a sq/bc+b sq/ca+c sq/ab.

Answer 1

Ans.

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

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