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1. x^2 + y^2 > z^2
Since x^2y^2>0, we don't know if x^4+y^4>z^4.
2. x + y > z
They could be different signs. Say both x and y are small positive numbers and z is a large negative. Then x^4+y^4 could be smaller than z^4. But the opposite is also possible. So insufficient.
Not very easy to prove. The best way to go, in my opinion is by counter examples. As long as you can find a set of numbers where both 1 and 2 are satisfied to answer No to the stem then you are all set. Because it is easy to find examples to say Yes to the stem, finding the No answer would mean the answer is not unique and that 1 and 2 combined are not sufficient.
Anyways you could try with the closest numbers such as 3, 3, 4, where 3+3>4, 3^2+3^2>4^2, but 3^4+3^4<4^4.
Therefore the answer is E.
Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.
09 Aug 2005, 20:54