Verified Answer :

W0lf93

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.

Answer:

Given the equation: \(-4\sqrt{x-3}=12\)          .....[1]

Solve for x;

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

\(\sqrt{x-3} = -3\)

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]

\(-4\sqrt{12-3}=12\)  

\(-4\sqrt{9}=12\)  

\(-4\cdot 3=12\)  

\(-12 =12\)   False.

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

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