1.
a/b+b/a≥2
a²/ab+b²/ab≥2 |*ab
a²+b²≥2ab
a²-2ab+b²≥0
(a-b)²≥0
2.
k+1/k≥2 |*k
k²+1≥2k
k²-2k+1≥0
(k-1)²≥0
3.
2a/(1+a²)≤1 |*(1+a²)
2a≤1+a²
a²-2a+1≥0
(a-1)²≥0
