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Problem 5 (Interesting Algebra Problem)

The numbers x, y, and z satisfy the equation

What is the value of k ?
Solution
We use the interesting (but not too-well known) algebraic fact that

To prove this statement, we start with the identity ab= ab and write

In our problem, we are given

If we apply our basic algebraic law (1) to (2-a), we have

Hence, the numerators must be equal, giving k = 18.

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Last modified on Tuesday, January 12, 1999