Question

A+b+c=0 then a^2/bc +b^2/ca +c^2/ab

Answer 1

Answer:

3

Step-by-step explanation:

Given :

If a + b + c = 0,

Then, the value of : $\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab}$

Solution :

We know that,

if a + b + c = 0,

then, a³ + b³ + c³ = 3abc .

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$\frac{a^2}{bc} + \frac{b^2}{ac} + \frac{c^2}{ab}$

⇒ $\frac{a^2}{bc} \times \frac{a}{a} + \frac{b^2}{ac} \times \frac{b}{b} + \frac{c^2}{ab} \times \frac{c}{c}$

⇒ $\frac{a^3}{abc} + \frac{b^3}{abc} + \frac{c^3}{abc} = \frac{a^3 + b^3 + c^3}{abc} = \frac{3abc}{abc} = 3$