What is an extraneous solution? a solution that was found due to an arithmetic error a solution that satisfies the original equa

Question

sattari [20]

3 years ago

10

What is an extraneous solution? a solution that was found due to an arithmetic error a solution that satisfies the original equa

tion an apparent solution that is not a real number an apparent solution that does not satisfy the original equation

Mathematics

2 answers:

lesantik [10] · Answer 1 · 2022-05-30T07:01:50+03:00

Answer:

an apparent solution that does not satisfy the original equation

Step-by-step explanation:

Usually, an extraneous solution is introduced by the solution process. Sometimes it takes the form of multiplying an equation by 0, often the result of eliminating the denominators of rational functions.

Other times, it takes the form of adding branches to a function that are unintended or undefined. (Squaring a square root will often introduce "solutions" that require the square root to be a negative value.) The attached graph shows that x=4 is an extraneous solution to ...

√x = x-6

It shows up when the equation is squared:

x = x² -12x +36 ⇒ (x -9)(x -4) = 0

The "solution" x=4 is extraneous because it does not satisfy the original equation.

As in this graphed example, using graphical methods to find solutions can often avoid extraneous solutions.