Question

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

Answer 1

Answer:

There is no solution for the given radical equation.

x = 225/16 is an extraneous solution.

Step-by-step explanation:

The given equation is $-4\sqrt x-3=12$

Add 3 to both sides of the equation

$-4\sqrt x=15$

Squaring both sides

$16x=225$

Divide both sides by 16

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

Substituting back the value of x in original equation to check the extraneous solution.

 $-4\sqrt (\frac{225}{16})-3=12\\\\-4\cdot\frac{15}{4}-3=12\\\\-15-3=12\\\\-18=12$

Since -18≠ 12. Hence, the value of x does not satisfy the equation.

Therefore, x = 225/16 is an extraneous solution.