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Part of 1998 Putnam

Problems(2)

Putnam 1998 A1

Source:

10/23/2012
A right circular cone has base of radius 1 and height 3. A cube is inscribed in the cone so that one face of the cube is contained in the base of the cone. What is the side-length of the cube?
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1998 Putnam B1

Source:

4/19/2013
Find the minimum value of (x+1/x)6−(x6+1/x6)−2(x+1/x)3+(x3+1/x3)\dfrac{(x+1/x)^6-(x^6+1/x^6)-2}{(x+1/x)^3+(x^3+1/x^3)} for x>0x>0.
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