Question-173610

Question Number 173610 by AgniMath last updated on 14/Jul/22

Answered by okbruh123 last updated on 14/Jul/22

M e t h o d 1 :

a s f a r a s i k n o w, t h i s i s p r o b l e m o f p r m o .

i t s o b j e c t i v e e x a m, s o t a k e a n y a, b, c f o l l o w i n g Σ a = 0

{l e t}^{'} s s a y - 3, + 1, + 2

y o u l l g e t \frac{9}{2} + \frac{1}{- 6} + \frac{4}{- 3} = \frac{27 - 1 - 8}{6} = 3

A l i t e r :

i f u w a n n a d o l e g i t,

\Rightarrow \frac{{(b + c)}^{2} a + {(a + c)}^{2} b + {(a + b)}^{2} c}{a b c}

\Rightarrow a + b + c = 0 \Rightarrow b + c = - a a n d s y m m e t r i c a l l y y o u c a n s o l v e f o r a + c a n d a + b

\Rightarrow \frac{a^{3} + b^{3} + c^{3}}{a b c} \Rightarrow \frac{\underset{= 0}{\underset{⏟}{(a + b + c)}} (a^{2} + b^{2} + c^{2} - a b - b c - c a) + 3 a b c}{a b c}

\Rightarrow \frac{3 a b c}{a b c} = 3

Commented by Tawa11 last updated on 14/Jul/22

Great sir

Answered by behi834171 last updated on 14/Jul/22

a + b + c = 0 \Rightarrow Σ a^{3} = 3 a b c

L H = Σ \frac{{(- a)}^{2}}{b c} = Σ \frac{a^{2}}{b c} = \frac{Σ a^{3}}{a b c} = \frac{3 a b c}{a b c} = 3 .