MATC Mathematics Club
Volume
8 Solutions Page
The Puzzle Corner of the MATC Mathematics Club
Madison Area Technical College
Madison, Wisconsin
Spring 2005 Problem Sets 
Problem Set #1, Volume #08 
1. Find all possible sets
of four consecutive integers having the property that the sum of the cubes of
the smallest three is equal to the cube of the largest.

2. Find the value of k
for which the two equations (x  2)^{4}  (x  2) = 0 and x^{2}  kx + k = 0 have two roots in common.

3. Find all ordered pairs
of integers (x, y) which satisfy x^{2} + 4x + y^{2} = 9.

4. The sum of the ages of
the members of a family is currently 75 years, where the family consists of a
mother, father, son, and daughter. Six years ago, the sum of the ages of
the family members was 53 years. If the father is four years older than
the mother, and the daughter is three years older that the son, find the current
age of the father.

5. Express in simplest
form:

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