Question

The sum of two positive numbers is 4 and the sum of their cubes is 28. What is the product of the two numbers?

Answer 1

3

Explanation:

system of equations:

`a+b=4`

`a^3+b^3=28`

`a=4-b`

plug in for a in other equation and solve

`(4-b)^3+b^3=28`

`64-48b+12b^2-b^3+b^3=28`

`64-48b+12b^2=28`

`0=36-48b+12b^2`

`0=3-4b+b^2`

`0=(b-3)(b-1)`

`b = 3`

or

`b=1`

plug into other equation to get a

`a=4-b=4-3=1`

or

`a=4-b=4-1=3`

multiply together

`1*3=3`