Question

Which of the following is an extraneous solution of mc015-1.jpg? x = –12 x = –3 x = 3 x = 12

Answer 1

The answer
the full the question is as follow:
Which of the following is an extraneous solution of (45 - 3x)^1/2 =x -9

for solving such an equation, this is the method:

finding the squared value of each member of the equation
[(45 - 3x)^1/2 ]²  = (x -9)²   (E)

extend each value of the member
[(45 - 3x)^1/2 ]² = 45 - 3x, because   (sqrt a )² = a
the condition is 45 - 3x≥0 ( because of the square root)
it means  - 3x≥ -45 and  x ≤ 15

(x -9)² = x²-18x + 81

so 45 - 3x = x²-18x + 81, this is equivalent to x² - 15x  +36 =0

this equation should solve for x, for finding the help

Delta = 15² - 4*36 = 81, so x = - (-15) - sqrt (81)  /  2 *1=15-9 /2= 3

                                      and x = - (-15) +sqrt (81)  /  2 *1= 15 +9/2= 24/2=12

for x= 12, the equation given above ( equation E) has no solution, because 
we can find 3=9

so an extraneous solution is x = 12