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

Question

asked May 13, 2018 26.0k views

2 Answers

Ali Navidi · Answer 1 · 2018-05-13T20:54:52+0000

Answer:

x=(225)/(16) is an extraneous solution.

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,

(16)/(16)x=(225)/(16)

x=(225)/(16)

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

$-4\sqrt ((225)/(16))-3=12$

-4*(15)/(4)-3=12

-15-3=12

$-18\\eq12$

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

So,
x=(225)/(16) is an extraneous solution.