Which statement best reflects the solution(s) of the equation?

(sqrt(2x−4))−x+6=0

there is only one solution: x = 10.
the solution x = 0 is an extraneous solution.

there is only one solution: x = 10.
the solution x = 4 is an extraneous solution.

there is only one solution: x = 4.
the solution x = 10 is an extraneous solution.

there are two solutions: x = 4 and x =10.

Option D. is the answer

Step-by-step explanation:

The given expression is

We further solve the given equation,

(2x - 4) = (x-6)²

x²- 12x + 36 - 2x + 4 = 0

x² - 14x + 40 = 0

x² - 10x - 4x + 40 = 0

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

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

(x - 4) = 0 ⇒ x = 4

Or (x - 10) = 0

⇒ x = 10

Now we put the value of x = 4 in the equation,

=

=

= 2 - 4 + 6

= 0

For x = 10

= 4 - 10 + 6

= 0

Therefore, there are two solutions x = 4, 10

Option D will be the answer.

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