Question 478287: The sum of the positive integers is 8 and the sum of their cubes is 152. what is the product of the two numbers?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The sum of the positive integers is 8 and the sum of their cubes is 152. what is the product of the two numbers?
----
Equations:
x + y = 8
x^3+y^3 = 152
----
Divide 1st into 2nd to get:
x^2-xy+y^2 = 19
----
Substitute for "x" and solve for "y":
(8-y)^2 - (8-y)y + y^2 = 19
64 -16y+y^2-8y+y^2 + y^2 = 19
---
3y^2 - 24y + 45 = 0
-------------
y^2 - 8y + 15 = 0
(y-3)(y-5)
---
If y = 3, x = 5
If y = 5, x = 3
===================
Cheers,
Stan H.
|
|
|
