An extraneous solution to a problem or equation is one that it introduced by the process of solving the problem, rather than being an essential element of the problem itself. It is usually detected by substituting the answers obtained back into the original equation, when extraneous solutions give incorrect or inconsistent results.

Let's take a simple example - solve √(x + 1) = x - 2

Square both sides x + 1 = (x - 2)² = x² - 4.x + 4

Rearrange to x² - 5.x + 3 = 0

which has two solutions from the quadratic formula

(a) x = (5 + √13)/2 and (b) x = (5 - √13)/2

Substitute these separately into the original equation and we obtain

(a) +2.3028 = +2.3028

(b) +1.3028 = -1.3028

Clearly answer (b) is incorrect, and represents the additional or extraneous solution introduced by the process of squaring the equation in the first step of its solution above. Yet another reason why you should always check your answers before submitting them for general inspection!