Hint to puzzle 44: Sum of two powers 2
The result is trivially true if x 
1.
When x < 1, begin by using Mitrinovic's generalization of Bernoulli's inequality on (1 + x/y)1/x.
The result is trivially true if x 1.
When x < 1, begin by using Mitrinovic's generalization of Bernoulli's inequality on (1 + x/y)1/x.