Final answer:
The given equation (1/√(x+2)) + 2 = 6 does not yield any of the provided multiple-choice options when solved. After isolating the variable and simplifying it, we find that x = -31/16, which does not match any of the available choices and is negative, not fitting the domain of a square root.
Step-by-step explanation:
To solve the equation (1/√(x+2)) + 2 = 6, follow these steps:
Subtract 2 from both sides of the equation to isolate the fraction on one side: (1/√(x+2)) = 4.
Multiply both sides by √(x+2) to eliminate the denominator: 1 = 4√(x+2).
Divide both sides by 4 to solve for the square root of x+2: 1/4 = √(x+2).
Square both sides to remove the square root: (1/4)² = x + 2.
Calculate (1/4)² which equals 1/16 and subtract 2 from both sides: 1/16 = x + 2 - 2.
Simplify to find the value of x: 1/16 - 32/16 = x.
Subtract the fractions: x = -31/16, which is a negative value and thus not viable since we're looking for a non-negative solution as per the domain of a square root.
In this case, there is clearly a misunderstanding because the results do not match any of the provided choices (a. 1 b. 2 c. 3 d. 4). However, there seems to be an error in the transcription of the problem since no non-extraneous solution exists within the given options.