Question

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

Answer 1

Given the equation:
`-4√(x-3)=12` .....[1]

Solve for x;

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

`√(x-3) = -3`

Squaring both the sides we get;

`x-3 = (-3)^2`

or

`x -3 = 9`

Add 3 both sides we get;

`x -3+3= 9+3`

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]

`-4√(12-3)=12`

`-4√(9)=12`

`-4\cdot 3=12`

`-12 =12` False.

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

Answer 2

4*sqrt(x-3)= 12. On squarng both the sides, we get, 16.(x-3) =144. or (x-3)= 144/16 = 9 or we can say that x = 3+9 = 12. Thus, x = 12 and it is not an extraneous solution. It would have been extraneous if x would have been 3.