Solve an equation with three variables

$\sqrt{x - 1} + \sqrt{y} + \sqrt{z + 1} = \frac{1}{2}$ (x + y + z + 3) )

$2 \sqrt{x - 1} + 2 \sqrt{y} + 2 \sqrt{z + 1} = (x + y + z + 3)$

$(x + y + z + 1 + 1 + 1) - 2 \sqrt{x - 1} - 2 \sqrt{y} - 2 \sqrt{z + 1} = 0$

Reordering:

$x - 2 \sqrt{x - 1} + 1 + y - 2 \sqrt{y} + 1 + z - 2 \sqrt{z + 1} + 1 = 0$

$(x - 1) - 2 \sqrt{x - 1} + 1 + y - 2 \sqrt{y} + 1 + (z + 1) - 2 \sqrt{z + 1} + 1 = 0$

$(\sqrt{x - 1} - 1) ^ {2} + (\sqrt{y} - 1) ^ {2} + (\sqrt{z + 1} - 1) ^ {2} = 0$

$(\sqrt{x - 1} - 1) = 0$ and $(\sqrt{y} - 1) = 0$ and $(\sqrt{z + 1} - 1) = 0$

Therefore x = 2, y = 1, z = 0.

n = $\frac{1}{2}$ (x + y + z + 3)

n = $\frac{1}{2}$ (2 + 1 + 0 + 3) = 6 / 2 = 3