Question

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Solve for x and show your steps. Is the solution extraneous? Check your work to show how you determined if the solution is extraneous or not.

Square Root 3x+12 = 9

Answer 1

x = 23; not extraneous

Explanation:

A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.

Solution

Squaring both sides of the given equation, we get ...

√(3x +12) = 9

3x +12 = 81 . . . . . . square both sides

x +4 = 27 . . . . . . . divide by 3

x = 23 . . . . . . . . . . subtract 4

Check

There is only one solution, and it satisfies the equation:

√(3×23 +12) = √81 = 9

The solution x = 23 is not extraneous.