Question

$\text{If} \: \: a+b+c = 0 \: \: \text{find value of} \\ ( \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ca} + \frac{ {c}^{2} }{ab} )$

Answer 1

It is given that the value of a + b + c is 0.


= > a + b + c = 0

= > a + b = - c

= > ( a + b )^3 = ( - c )^3

= > a^3 + b^3 + 3ab( a + b ) = - c^3


From above, a + b = - c

= > a^3 + b^3 + 3ab( - c ) = - c^3

= > a^3 + b^3 - 3abc = - c^3

= > a^3 + b^3 + c^3 = 3abc

$\implies \dfrac{ {a}^{3} + {b}^{3} + {c}^{3} }{abc} = 3 \\ \\ \\ \implies \dfrac{ {a}^{3} }{abc} + \dfrac{ {b}^{3} }{abc} + \dfrac{ {c}^{3} }{abc} = 3 \\ \\ \\ \implies \dfrac{ {a}^{2} }{bc} + \dfrac{ {b}^{2} }{ac} + \dfrac{ {c}^{2} }{ab} = 3$



Hence, the required numeric value of $\dfrac{ {a}^{2} }{bc} + \dfrac{ {b}^{2} }{ac} + \dfrac{ {c}^{2} }{ab}$ is 3.

Answer 2

➡➡$<b><u>hey buddyy❤❤❤$

==>> Hey buddy,,....

given= a + b + c = 0,,,

$( \frac{ {a}^{2} }{bc} + \frac{ {b}^{2} }{ca} + \frac{ {c}^{2} }{ab} )$...

plz refer attachment ...

and ans will be 3...
$<i><b><u><marquee>rgrds,,, @stylg...$