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.
+128460 We have that
a^3 + b^3 = 152 and a + b = 8
So we have that
152 = (a + b)^3 - 3ab ( a + b)
152 = (8)^3 - 3ab (8)
152 = 512 - 24ab rearrange as
24ab = 512 - 152
24ab = 360 divide both sides by 24
ab = 15 → (the product of the two numbers )
BTW.....the numbers are 3 and 5 ....
