Find two consecutive numbers whose cubes differ by 631

1 answer:

4 0

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

<em>Therefore, the two consecutive numbers are 14 and 15.</em>

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