Question

Es urgente : a+b+c=0 hallar: E==(a^3+b^3+c^3)/abc+(a+b)/c+(b+c)/a+(a+c)/b

Answer 1

Si:

$a + b + c = 0$

Se cumple:

${a}^{3} + {b}^{3} + {c}^{3} = 3abc$

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

...

$a + b = - c$

$b + c = - a$

$a + c = - b$

...

Reemplazando:

$E = (3) + \frac{ (- c)}{c} + \frac{( - a)}{a} + \frac{( - b)}{b}$

$E = 3 - 1 - 1 - 1$

$E = 0$