Good problem. The thing to remember is that the principals that guide exponential relationships don't hold true when you're manipulating with other operations.
Statement 1 tells us that x^2 + y^2 > z^2. And I think the trap to watch for here is that while if x^2 > z^2 then you know that x^4 > z^4, the same is not true when you're adding exponential variables.
Let's say that 4^2 +4^2 > 5^2 because 16 + 16 > 25. But what happens when you raise to the fourth? 256 + 256 > 625? No! Therefore, insufficient.
Statement 2 has the same problem in even simpler terms. x + y > z could be 4 + 5 > 2. But it could also be 1 + 2 > -20. And so you'd have two different solutions in the original question. Therefore, insufficient.
