Tag Archives: intersection of graphs

Product of Consecutive Integers

How many integer pairs satisfy the equation ? Source: NCTM Mathematics Teacher, September 2006 Solution We construct products of positive consecutive integers and see which ones if any can be expressed as a power of . is the only such … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , , | Leave a comment

Real Solutions (x,y)

How¬† many real solutions are there that satisfy the two equations and ? Source: NCTM Mathematics Teacher, September 2006 Solution The graph of is a circle centered at the origin and radius = . The graph of is a hyperbola … Continue reading

Posted in Problem solving | Tagged , , , , , , , | Leave a comment

Absolute Value Function

What is the area of the region bounded by the graph of ? Source: NCTM Mathematics Teacher, October 2006 Solution If and If and If and If and The four graphs intersect and form a square of side length . … Continue reading

Posted in Problem solving | Tagged , , , , , , , | 1 Comment

2x^2=3y^2

What is the only pair of integers for which twice the square of the first equals three times the square of the second? Source: NCTM Mathematics Teacher, October 2006 Solution We are looking for integers such that . If , … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , , | Leave a comment

Distance From Zero

Find the product of all real values of that satisfy the equation . Source: NCTM Mathematics Teacher, January 2006 SOLUTION One way to interpret the absolute values and is to think of them as the distances from point to point … Continue reading

Posted in Problem solving | Tagged , , , , , , , , , , | Leave a comment