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Problems > High School Math > 2008

How Many Solutions?

1. Unique Solution: For which real numbers, a, does the equation


a 3x + 3-x = 3

 

have a unique solution?

 

Source: Crux Mathematica, April 2002, from a Finnish high school math contest.

 

 

2. Two Solutions: For what values of m does sqrt(x-5)=mx+2 have two solutions?

 

 

Source: unknown

 



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