The difference in volumes of two cubes is 152 m 3 and the difference in their one face areas is 20 m 2. If the sum of their edge is 10 m, the product of their edge is?

Let the edges of the two cubes be x and y metres
Then, x³ - y³ = 152
and x² - y² = 20
Also, x + y = 10
So, x - y = (x² - y²) / (x + y) = 20/10 = 2
Now, (x³ - y³) / (x - y) = 152/2
⇒ x² + y² + xy = 76
⇒ (x + y)² - xy = 76
⇒ xy = (x + y)² - 76 = (10)² - 76 = 24