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by harryh
Tue Sep 26, 2006 7:45 am
Forum: Number
Topic: Log to base pi
Replies: 7
Views: 5316

How would you have determined the cube roots of 8+[radic]189 and -8+[radic]189? I wouldn't. If I suspected that their difference is 1, I would check whether p=8, q=189 satisfies 8p 3 +15p 2 +6p-1=27q. [Call x=√q + p, y=√q - p. Hence x-y=2p and xy=q-p 2 . If x 1/3 -y 1/3 =1, the identity x-y=(x 1/3 ...