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
