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in Linear Inequations by (23.5k points)
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If a, b, c, x, y, z are all positve real numbers, then

\(\big(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}\big)\big(\frac{a}{x}+\frac{b}{y}+\frac{c}{z}\big)≥\)

(a) 8 

(b) 64 abc 

(c) xyz 

(d) 9

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(d) 9

a, b, c, x, y, z being all positive real numbers

⇒ \(\frac{x}{a},\frac{y}{b},\frac{z}{c},\frac{a}{x},\frac{b}{y},\frac{c}{z}\) are all positive real numbers. 

Now applying the AM – GM inequality, we have

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