Question

(sqrt x) -1 = sqrt( x -(sqrt x+7) - 1)

Answer 1

Решение во вложенной картинке.

 

Answer 2

Let's start by simplifying the expression on the right side of the equation:

sqrt(x - (sqrt(x) + 7) - 1) = sqrt(x - sqrt(x) - 8)

We can simplify this further by recognizing that x - sqrt(x) can be factored as sqrt(x) * (sqrt(x) - 1):

sqrt(x - sqrt(x) - 8) = sqrt(sqrt(x) * (sqrt(x) - 1) - 8)

Now, we can substitute this expression back into the original equation:

sqrt(x) - 1 = sqrt(sqrt(x) * (sqrt(x) - 1) - 8)

Squaring both sides of the equation, we get:

x - 2sqrt(x) + 1 = sqrt(x) * (sqrt(x) - 1) - 8

Expanding the right side of the equation, we get:

x - 2sqrt(x) + 1 = x - sqrt(x) - 8

Subtracting x from both sides of the equation, we get:

-2sqrt(x) + 1 = -sqrt(x) - 8

Adding sqrt(x) and 8 to both sides of the equation, we get:

sqrt(x) = 9

Squaring both sides of the equation, we get:

x = 81

Therefore, the solution to the equation is x = 81.