The Goal

Find the distance D between the points (x,0,0) and (x,y,z) in 3-space.

The Mistake

Find the algebra mistake:

(Roll the mouse over the algebra to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

An Explanation

The mistake is in the final step - it is incorrect to distribute the square root over the sum. That is:

Try it with some numbers to convince yourself: let A=1 and B=1. The left side is √2, while the right side is 2. One counterexample disproves a general formula.