Question

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : Their product

Answer 1

Given difference between two positive numbers is 4 and difference between their cubes is 316.
Let the positive numbers be a and b
a - b = 4
a³ - b³ = 316
Cubing both sides,
(a - b)³ = 64
a³ - b³ - 3ab(a - b) = 64

Given a³ - b³ = 316
So 316 - 64 = 3ab(4)
252 = 12ab
So ab = 21; product of numbers is 21