Question

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.

Answer 1

Product of the numbers is 15

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