Given the equation −4 * sqrt (x-3) = 12, solve for x and identify if it is an extraneous solution.

Given the equation:          .....[1]

Solve for x;

Divide both sides by -4 in [1];  we get;

Squaring both the sides we get;

or

Add 3 both sides we get;

Simplify:

x= 12

Extraneous solution states that it is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.

Substitute  x= 12 in [1]

  False.

Therefore, the value of x is 12 and it is an extraneous solution.