If a + b + c = 0, then the value of (a²)/(bc) + (b²)/(ca) + (c²)/(ab) is :

If a + b + c = 0, then the value of (a²)/(bc) + (b²)/(ca)…

If a + b + c = 0, then the value of $\frac{{{a^2}}}{{bc}} + \frac{{{b^2}}}{{ca}} + \frac{{{c^2}}}{{ab}}$ is :

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Correct answer: B

Explanation

The correct answer is Option 2 i.e. 3.

$\frac{{{a^2}}}{{bc}} + \frac{{{b^2}}}{{ca}} + \frac{{{c^2}}}{{ab}}$ can be expressed as (a³ + b³ + c³)/abc

We know, (a + b + c)³ = (a + b + c)(a² + b² + c² - ab - bc - ca) + 3abc

and a + b + c = 0,

So,

(a³ + b³ + c³)/abc = 0 + 3 = 3