let a,b,c ∈R determine the minimum value ((3a)/(b+c))+((4b)/(a+c))+((5c)/(a+b))


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Question Number 99117 by M±th+et+s last updated on 18/Jun/20

$l e t a, b, c \in R d e t e r m i n e t h e m i n i m u m$ $v a l u e$ $\frac{3 a}{b + c} + \frac{4 b}{a + c} + \frac{5 c}{a + b}$
	Answered by MJS last updated on 19/Jun/20

	$- \infty < \frac{3 a}{b + c} + \frac{4 b}{a + c} + \frac{5 c}{a + b} < + \infty$ $i . e . let a = 0 \land b = 1$ $\frac{3 a}{b + c} + \frac{4 b}{a + c} + \frac{5 c}{a + b} = \frac{5 c^{2} + 4}{c}$ $\lim_{c \to \pm \infty} \frac{5 c^{2} + 4}{c} = \pm \infty$
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