If \( a, b, c, d \) are four positive numbers then
\( \mathrm{P} \)...
If \( a, b, c, d \) are four positive numbers then
\( \mathrm{P} \)
(a) \( \left(\frac{a}{b}+\frac{b}{c}\right)\left(\frac{c}{d}+\frac{d}{e}\right) \geq 4 \cdot \sqrt{\frac{a}{e}} \)
(b) \( \left(\frac{a}{b}+\frac{c}{d}\right)\left(\frac{b}{c}+\frac{d}{e}\right) \geq 4 \cdot \sqrt{\frac{a}{e}} \)
(c) \( \frac{a}{b}+\frac{b}{c}+\frac{c}{d}+\frac{d}{e}+\frac{e}{a} \geq 5 \)
(d) \( \frac{b}{a}+\frac{c}{b}+\frac{d}{c}+\frac{e}{d}+\frac{a}{e} \geq \frac{1}{5} \)
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