Question

if a+b+c=0 then a^2/bc+b^2/ac+c^2/ab=?​

Answer 1

We know that,

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

Therefore,

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

Since, a+b+c is zero therefore, a³+b³+c³ becomes 3abc using the above equation.

Therefore our equation becomes,

$\frac{3abc}{abc} = 3$