Common Algebra Mistakes
Example: Solving a Quadratic Equation 
The Goal
Find all pairs (x,y) (for x and y both real numbers) satisfying the equation:
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
There is no mistake in the algebra, only a failure to notice at the start that x^{2} + 4y^{2} can only be zero if both x and y are zero. 
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