Use the identity a^3+b^3 = (a+b) ^3 - 3ab (a+b) to determine the product of the two numbers if the sum of the cubes of the two numbers is 152 and the sum of the two numbers is 8.

Product of the numbers is 15

Step-by-step explanation:

Step 1:

Let the numbers be a and b. Given that, the sum of the cubes of the 2 numbers is 152 and the sum of the 2 numbers is 8. Form equations out of the given data.

⇒ a³ + b³ = 152 and a + b = 8

Step 2:

Use identity a³ + b³ = (a + b) ³ - 3ab (a + b). Substitute the values in this identity.

⇒ 152 = 8³ - 3ab (8) = 512 - 24ab

⇒ 24ab = 360

⇒ ab = 360/24 = 15