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for both options 1 and 2 lets take x=10, y=5 and z=-11 then we get answer for x^4 + y^4 > z^4 as NO and if we take x=10 y=5 and z =3 we get answer for x^4 + y^4 > z^4 as YES
Wow that's a tough one, I was trying to solve it algebraicly and couldn't so I googled it and found some info I thought I'd share:
1) It's pretty much impossible to solve this one algebraicly < 2 mins 2) Picking numbers is the best way 3) Try to use small numbers so you can generated 4th power exponents without too much trouble.
The solution I saw did it this way: Statement 1) Used x and y=3 and z=4 to prove the answer No. (yes is easy) Statement 2) This one was easy because just make x and y small positive numbers (such as 1) and make z a large negative number such as -1000 to prove the answer No.
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