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 x2 + 4y2 can only be zero if both x and y are zero.
(Once the algebra had been done, note that the quantity under the square root can only have a real value if x=0, and therefore also y=0.)

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