Question

Find two consecutive numbers whose cubes differ by 631

Answer 1

Let the two numbers be x and y, in which x is larger than y. From these variables, we can formulate the following equations:

x = y + 1  --> eqn 1
x³ - y³ = 631 --> eqn 2

Since there are two unknowns and two independent equations, this system is solvable. Substitute equation 1 to equation 2, then solve for y.

(y + 1)³ - y³ = 631
Solving for y,
y = 14
x = y + 1  = 14 + 1 = 15

Therefore, the two consecutive numbers are 14 and 15.