| x | y | |||
Dla dodatnich liczb x,y,z których iloczyn wynosi 1 udowodnij | + | + | ||
| y+z+1 | x+z+1 |
| z | ||
≥1 | ||
| x+y+1 |
| x | y | z | t | 4 | |||||
+ | + | + | ≥ | ||||||
| y+z+t | z+t+u | t+x+y | x+y+z | 3 |
| 1 | 1 | |||
Dalej u=1. Jeśli xyz=1, to x+y+z ≥ 3 i | ≤ | . | ||
| x+y+z | 3 |
| x | y | z | 1 | ||||
+ | + | + | |||||
| y+z+1 | z+1+u | 1+x+y | 3 |
| x | y | z | 1 | 4 | ||||||
≥ | + | + | + | ≥ | ||||||
| y+z+1 | z+1+u | 1+x+y | x+y+z | 3 |
| x | y | z | u | 4 | |||||
+ | + | + | ≥ | ||||||
| y+z+u | z+u+x | u+x+y | x+y+z | 3 |
| 8 | 1 | b | a | 8 | 12 | 4 | ||||||||
Teraz lewa strona = − | + | ( | + | + ...) ≥ − | + | = | ||||||||
| 3 | 3 | a | b | 3 | 3 | 3 |
| 5^2 | 52 |
| 2^{10} | 210 |
| a_2 | a2 |
| a_{25} | a25 |
| p{2} | √2 |
| p{81} | √81 |
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