let-a-b-c-R-determine-the-minimum-value-3a-b-c-4b-a-c-5c-a-b-

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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