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Answer
Para encontrar la ecuación con la raíz extránea
, evalúa cada ecuación con
y comprueba si cumple con la ecuación original.
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To identify an extraneous root, let’s consider the equation
. When we solve it, we find
. If we also plug this back into a more complex function or an equation with rational expressions, we might find that it doesn’t satisfy the original equation due to undefined values or contradictions, indicating that
is an extraneous solution. Always check the context of where the solutions apply!
For example, in rational expressions, if we had
and solved for
, we would find
but notice that it makes the denominator zero, proving it’s extraneous in that context. Never forget to check your solutions against the original equation!