Question

Given the equation −4 Square root of x minus 3= 12, solve for x and identify if it is an extraneous solution

Answer 1

I believe ur answer is 12 and is extraneous

Answer 2

Answer:

$x=\frac{225}{16}$ is an extraneous solution.      

Step-by-step explanation:

Given : Equation $-4\sqrt x-3=12$

To find : Solve for x and identify if it is an extraneous solution?

Solution :

Step 1 - Write the equation,

$-4\sqrt x-3=12$

Step 2 - Add 3 both sides,

$-4\sqrt x-3+3=12+3$

$-4\sqrt x=15$

Step 3 - Squaring both sides,

$(-4\sqrt x)^2=(15)^2$

$16x=225$

Step 4 - Divide both side by 16,

$\frac{16}{16}x=\frac{225}{16}$

$x=\frac{225}{16}$

For extraneous solution, Substitute the value of x back in the equation.

$-4\sqrt (\frac{225}{16})-3=12$

$-4\times\frac{15}{4}-3=12$

 $-15-3=12$

$-18\neq12$

The value of x does not satisfy the equation which means the value of x is an extraneous solution.

So, $x=\frac{225}{16}$ is an extraneous solution.