The distance between two points (x1, y1) and (x2, y2) is sqrt[(x2 - x1)^2 + (y2 - y1)^2]

Here we have A(0, 4) and B(x , 5). AB = 6

6 = sqrt[(0 - x)^2 + (4 - 5)^2]

=> 6 = sqrt (x^2 + 1)

=> 36 = x^2 + 1

=> x^2 = 35

=> x = sqrt 35 or -sqrt 35

**The value of x can be sqrt 35 or -sqrt 35**

Given the distance between A and B is 6 units.

We need to find the value of x.

We will use the distance between 2 points formula to find x.

==> D = sqrt(x-x2)^2 + (y1-y2)^2

==> 6 = sqrt( x-0)^2 + (4-5)^2

==> 6 = sqrt(x^2 + 1)

Now we will square both sides.

==> x^2 +1 = 36

==> x^2 = 35

==> x = +-sqrt35

**Then there are 2 possible values for x : x= { sqrt35, -sqrt35}**

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