Question

PLEASE ANSWER MY QUESTION I AM DESPERATE!!!!!!
URGENT 50 POINTS!!!
Which statement best reflects the solution(s) of the equation?
$\sqrt{2x-4} -x+6=0$

A.There is only one solution: x = 4.
The solution x = 10 is an extraneous solution.
B. There is only one solution: x = 10.
The solution x = 4 is an extraneous solution.
C. There are two solutions: x = 4 and x =10.
D. There is only one solution: x = 10.
The solution x = 0 is an extraneous solution.

Answer 1

Answer:

The answer is C

Step-by-step explanation:

First, let's solve the equation √(2x - 4) - x + 6 = 0:

√(2x - 4) - x + 6 = 0

Let's denote √(2x - 4) as y, then:

y - x + 6 = 0

y = x - 6

Now, we'll square both sides to eliminate the square root:

y^2 = (x - 6)^2

2x - 4 = x^2 - 12x + 36

0 = x^2 - 14x + 40

0 = (x - 4)(x - 10)

So, the solutions are x = 4 and x = 10.

Now let's go through the options:

A. There is only one solution: x = 4. The solution x = 10 is an extraneous solution. - This is incorrect because there are two solutions.

B. There is only one solution: x = 10. The solution x = 4 is an extraneous solution. - This is incorrect because there are two solutions.

C. There are two solutions: x = 4 and x = 10. - This is the correct statement as it accurately reflects the solutions of the equation.

D. There is only one solution: x = 10. The solution x = 0 is an extraneous solution. - This is incorrect because there are two solutions and x = 0 is not a solution mentioned in the calculation.