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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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