Find one pair of real numbers, $ (x, y),$ such that $x + y = 6$ and $x^3 + y^3 = 144.$

For this case we have the following system of equations:

x + y = 6

x ^ 3 + y ^ 3 = 144

Solving the system of equations graphically we have that one of the solutions is:

x = 3-root (5)

y = 3 + root (5)

Then, an ordered pair that satisfies both equations:

(x, y) = (3-root (5), 3 + root (5))

Answer:

(x, y) = (3-root (5), 3 + root (5))