If-a-b-c-0-then-a-b-b-c-a-c-abc-is-equal-to-

Question Number 21471 by Joel577 last updated on 24/Sep/17

If a + b + c = 0, then

\frac{(a + b) (b + c) (a + c)}{a b c} is equal to \dots

Answered by Tinkutara last updated on 24/Sep/17

a + b = - c

∴ \frac{(a + b) (b + c) (c + a)}{a b c} = \frac{(- c) (- a) (- b)}{a b c} = - 1

Commented by Joel577 last updated on 24/Sep/17

t h a n k y o u v e r y m u c h

Answered by Rasheed.Sindhi last updated on 25/Sep/17

\underline{An other way}

a + b + c = 0 \Rightarrow {\begin{cases} a = - (b + c) \\ b = - (a + c) \\ c = - (a + b) \end{cases}

\frac{(a + b) (b + c) (a + c)}{a b c} =

\frac{(a + b) (b + c) (a + c)}{- (b + c) . - (a + c) . - (a + b)} = - 1