Tìm x

To solve the equation x-√(x-2) = 4, we can start by isolating the square root term.

First, add √(x-2) to both sides of the equation:
x = 4 + √(x-2)

Next, square both sides of the equation to eliminate the square root:
x^2 = (4 + √(x-2))^2
x^2 = 16 + 8√(x-2) + (x-2)

Simplify the equation:
x^2 = x + 14 + 8√(x-2)

Now, isolate the square root term by subtracting x and 14 from both sides:
x^2 - x - 14 = 8√(x-2)

Square both sides of the equation again:
(x^2 - x - 14)^2 = (8√(x-2))^2
x^4 - 2x^3 - 27x^2 + 4x + 196 = 64(x-2)

Expand and simplify the equation:
x^4 - 2x^3 - 27x^2 + 4x + 196 = 64x - 128
x^4 - 2x^3 - 27x^2 - 60x + 324 = 0

At this point, we can try to factor the equation or use numerical methods to find the solutions.