Question

√(x - 5) = 5 - √x
a) x = 10
b) x = 25
c) x = 5
d) x = 0

Answer 1

After performing a series of steps to isolate x in the equation, we find that the original equation has no solution in real numbers, hence none of the given options is correct. The process of squaring both sides and manipulating the equation shows that x = 4, which does not satisfy the original equation.

Step-by-step explanation:

To solve the mathematical problem completely, we need to isolate the variable x in the equation √(x - 5) = 5 - √x. We'll go step by step:

1. First, square both sides of the equation to get rid of the square root terms:
   (x - 5) = (5 - √x)²
2. Expanding the right side gives:
   (x - 5) = 25 - 10√x + x
3. Now, isolate the square root term by moving all other terms to the opposite side:
   10√x = 25 - 5
   10√x = 20
4. Divide both sides by 10 to get the square root term by itself:
   √x = 2
5. Finally, square both sides again to solve for x:
   x = 4

However, x = 4 does not satisfy the original equation √(x - 5) = 5 - √x because when plugging it back in, we get √(-1) on the left, which is not possible in real numbers (since we are dealing with the principal square root). This means that there is no solution among the provided options, and so all options are incorrect.

Therefore, none of the provided options a) x = 10, b) x = 25, c) x = 5, or d) x = 0 are the correct option answer to the original equation.