Prove for every real $a,b$: $$a^4+b^4+1\ge a+b$$
What I've tried:
1.I checked how AM-GM may help but doesn't look like it's useful here.
- I've tried:
$$(a^2+b^2)^2 -2(ab)^2+1 \ge a+b$$
But unfortunately, I can't find any way to continue this.. I'm sure that this isn't too hard, it's just that "I'm not seeing it", I would appreciate if clues are given first so I can answer this myself.
*This exercise is from the TAU entry exams.