Find x and y such that x^3 + y^3 = 1729

To find the values of x and y that satisfy the equation x^3 + y^3 = 1729, we can use a technique called the Brute Force method or exhaustive search.

1. Begin by testing different values for x and y. Start with small integers and gradually increase the values until the equation is satisfied or you have exhausted all possible values.

2. You can start by trying different values of x from -10 to 10. For each value of x, calculate y using the equation y = (1729 - x^3)^(1/3).

3. Calculate the cube of each y value and add it to the cube of its corresponding x value. If the sum is equal to 1729, then x and y are the solutions to the equation.

Here is a Python code snippet that implements this approach:

```python
import math

def find_x_and_y():
for x in range(-10, 11):
y_cubed = 1729 - x ** 3
y = round(math.pow(y_cubed, 1/3))
if x**3 + y**3 == 1729:
return x, y

x, y = find_x_and_y()
print("x =", x)
print("y =", y)
```

Running this code will output the values of x and y that satisfy the equation x^3 + y^3 = 1729. In this case, there is only one solution: x = 1 and y = 12.