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This is a quadratic equation in terms of x and y. To solve for x and y, we can rewrite the equation as follows:

x² + (4y - 2z)x + (4y² - 4yz + y² + 1) = -z² - √x

Now, we can use the quadratic formula to solve for x in terms of y and z:

x = [-4y + 2z ± √((4y - 2z)² - 4(4y² - 4yz + y² + 1)(-z² - √x))] / 2

Simplifying further, we get:

x = [-4y + 2z ± √(16y² - 16yz + 4z² + 16y² - 16yz - 4y² - 4y² - 4 + 4z² + 16yz + 4y² + 4)] / 2

x = [-4y + 2z ± √(32y² + 4z² - 4)] / 2

Similarly, we can solve for y in terms of x and z:

y = [-2z ± √(4z² - 4x - 4y² - 1)] / 8

These are the solutions for x and y in terms of z.