Given $$ a+b+c=0 $$ , $$ abc $$ ≠ 0 , $$ a, b,c, $$ are not equal to each other, find the value of
$$ \dfrac{a^2}{bc} +\dfrac{b^2}{ac} +\dfrac{c^2}{ab} $$

Question

Given $$ a+b+c=0 $$ , $$ abc $$ ≠  0  , $$ a, b,c, $$ are not equal to each other, find the value of 
$$ \dfrac{a^2}{bc}  +\dfrac{b^2}{ac}  +\dfrac{c^2}{ab}  $$

Uniteasy Admin · Accepted Answer

$$ \dfrac{a^2}{bc} +\dfrac{b^2}{ac} +\dfrac{c^2}{ab}  =\dfrac{a^3+b^3+c^3}{abc} $$
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$$ \because a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^3-ab-bc-ac) $$
$$ \quad $$ and
$$ a+b+c=0 $$
$$ 	herefore  a^3+b^3+c^3-3abc=0 $$
$$ \dfrac{a^3+b^3+c^3}{abc} =3 $$

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