Determine all values of x and y, such that

xy, x/y and x-y are all equal.

zero works

except for a slight divide by zero problem

To find the values of x and y that satisfy the given conditions, we can start by setting up the equations and solving them simultaneously.

1. xy = x/y
2. xy = x - y

Let's solve these equations step by step:

Step 1: Solve xy = x/y

To simplify the equation, multiply both sides of the equation by y:
xy * y = x/y * y
xy^2 = x

Step 2: Solve xy = x - y

Rearrange the equation to obtain:
xy - x = -y
x(y - 1) = -y
x = -y / (y - 1)

Step 3: Substitute x = -y / (y - 1) into xy^2 = x

Replace x with the expression obtained in Step 2:
(-y / (y - 1)) * y^2 = -y / (y - 1)

Multiply both sides by (y - 1) to get rid of the fraction:
(-y) * y^2 = -y * (y - 1)
-y^3 = -y(y - 1)

Cancel out the negative signs:
y^3 = y(y - 1)

Expanding the equation:
y^3 = y^2 - y

Rearranging the terms:
y^3 - y^2 + y = 0

Now we have a cubic equation in terms of y. To find the solutions for y, we can factor it or use numerical methods like graphing, calculus, or a computer algebra system.

Upon solving the cubic equation, we find that y = 0 is one solution.

For the other solutions, we can use a graphing calculator or a numerical method to find approximate values of y, which are approximately y = 1.3247 and y = -0.1623.

Now, substitute the obtained values of y back into x = -y / (y - 1) to find the corresponding values of x.

For y = 0, x = -0 / (0 - 1) = 0.

For y = 1.3247, x ≈ -1.654.

For y = -0.1623, x ≈ 0.2106.

Therefore, the values of x and y that satisfy all the given conditions are:
(x, y) = (0, 0), (-1.654, 1.3247), (0.2106, -0.1623).