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
