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x^4+y^4

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x^4+y^4

by sk8ternite » Tue Jul 14, 2009 12:57 pm
x^4+y^4=100, then the greatest possible value of x is between?
(a) 0 and 3
(b) 3 and 6
(c) 6 and 9
(d) 9 and 12
(e) 12 and 15

answer is b. Why not a?
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by truplayer256 » Tue Jul 14, 2009 1:09 pm
x^4+y^4=100

x would be the greatest when y is the least. Let's say y is less than or equal to one and greater than or equal to -1. This means that x would be an integer equal to or greater than the fourth root of 99. The fourth root of 99 should be somewhere between 3 and 4 since 3^4 is 81 and 4^4 is 256. Now if y was a fraction less than one and greater than -1, then the fourth root of the value of x you get obviously has to be greater than the fourth root of 99. The answer is B.
Last edited by truplayer256 on Tue Jul 14, 2009 1:13 pm, edited 2 times in total.
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by sk8ternite » Tue Jul 14, 2009 1:12 pm
oh i got it, I was thinking only in integers
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