You are given that x=(2x^2-x+8)y.(1)show,by the method of completing the square that (x-1+y)^2 divided by 4y,=1+2y-63y^2 divided by 16y^2

To show that (x-1+y)^2/4y = 1+2y-63y^2/16y^2 using the method of completing the square, we will follow the steps below:

Step 1: Start with the given equation x = (2x^2 - x + 8)y.

Step 2: Expand the equation on the right-hand side:

2x^2 - x + 8 = (x-1)^2 + 2y - 63y^2/16y^2

Step 3: Divide both sides of the equation by 4y:

(x-1+y)^2 / 4y = (x-1)^2 / 4y + 2y - 63y^2 / (16y^2 * 4y)

Step 4: Simplify the right-hand side:

(x-1+y)^2 / 4y = (x-1)^2 / 4y + 2y - 63y^2 / (64y^3)

Step 5: Reduce the fractions:

(x-1+y)^2 / 4y = (x-1)^2 / 4y + 2y - 63 / 64y

Step 6: Combine the fractions:

(x-1+y)^2 / 4y = [(x-1)^2 + 8y - 63] / 64y

Step 7: Simplify further:

(x-1+y)^2 / 4y = (x^2 - 2x + 1 + 8y - 63) / 64y

(x-1+y)^2 / 4y = (x^2 - 2x - 62 + 8y) / 64y

Step 8: Use the given equation, x = (2x^2 - x + 8)y, to substitute for x:

(x-1+y)^2 / 4y = ((2(2x^2 - x + 8)y) - 2x - 62 + 8y) / 64y

Simplifying further would require additional information about the value of x or y.