If a + b + c = 0, then (((a + b)(b + c)(a + c))/(abc)) is equal to ...


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

$If a + b + c = 0, then$ $\frac{(a + b) (b + c) (a + c)}{a b c} is equal to . . .$
	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
	$An other way _(−) a+b+c=0⇒ { ((a=−(b+c))),((b=−(a+c))),((c=−(a+b))) :} (((a + b)(b + c)(a + c))/(abc))= (((a + b)(b + c)(a + c))/(−(b+c).−(a+c).−(a+b)))=−1$
	$\underline{An other way}$ $a + b + c = 0 \Rightarrow {\begin{cases} a = - (b + c) \\ b = - (a + c) \\ c = - (a + b) \end{cases}$ $\frac{(a + b) (b + c) (a + c)}{a b c} =$ $\frac{(a + b) (b + c) (a + c)}{- (b + c) . - (a + c) . - (a + b)} = - 1$
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