The equation to be solved is (x-4)^1/2=1/(x-4)
(x-4)^1/2=1/(x-4)
square both the sides
=> x - 4 = 1 / (x - 4)^2
=> (x - 4)^3 = 1
=> 1 - (x - 4)^3 = 0
=> (1 - (x - 4))(1 + x - 4 + (x - 4)^2) = 0
=> (1 - x + 4)(1 + x - 4 + x^2 + 16 - 8x) = 0
=> (-x + 5)(x^2 - 7x + 13) = 0
-x + 5 = 0
=> x = 5
x^2 - 7x + 13 = 0
=> x1 = 7/2 + sqrt(49 - 52) /2
=> x1 = 7/2 + i*(sqrt 3)/2
x2 = 7/2 - i*(sqrt 3/2)
The equation has the solutions x = (5, 7/2 + (sqrt 3)/2, 7/2 - (sqrt 3/2))
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