Question
If $a + b + c = 0,$ then $\Big(\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}\Big)=$
✓
Answer
$\Big(\frac{\text{a}^2}{\text{bc}}+\frac{\text{b}^2}{\text{ca}}+\frac{\text{c}^2}{\text{ab}}\Big)$
$=\frac{\text{a}^3+\text{b}^3+\text{c}^3}{\text{abc}}$
Since $a + b + c = 0,$ then $a^3 + b^3 + c^3 = 3abc$
Therefore,
$=\frac{3\text{abc}}{\text{abc}}$
$=3$
$=\frac{\text{a}^3+\text{b}^3+\text{c}^3}{\text{abc}}$
Since $a + b + c = 0,$ then $a^3 + b^3 + c^3 = 3abc$
Therefore,
$=\frac{3\text{abc}}{\text{abc}}$
$=3$
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