Question

√√x-a=x-4

If a= 2, what is the solution set of the equation
above?
A) (3,6)
B) (2)
C) (3)
D) (6)

Answer 1

To solve the equation, start by isolating the square root term and use algebraic steps to simplify the equation and solve for x. The solution set is {3, 6}.

Step-by-step explanation:

To solve the equation √√x-a=x-4, we can start by isolating the square root term. First, we square both sides of the equation to eliminate the outer square root: (√x-a)^2 = (x-4)^2. This simplifies to x - 2a√x + a^2 = x^2 - 8x + 16.

Next, we can rearrange the equation to isolate the square root term: 2a√x = x^2 - x + 16 - a^2.

Finally, we square both sides again and solve for x: (2a√x)^2 = (x^2 - x + 16 - a^2)^2. From the given value of a = 2, we substitute this into the equation and solve for x. The solution set is {3, 6}.

Learn more about Solving equations involving square roots