- #1
albertrichardf
- 165
- 11
Homework Statement
##1729## can be written as ##12^3 + 1^3## and ##9^3 + 10^3## and ##7(10 + 9)(12 + 1)##. If
##x^3 + (7 - x)^3 = 1729##, use the above to find ##x##. ##x## is a non-integer
Homework Equations
##1729 = 12^3 + 1^3 = 9^3 + 10^3 = 7(10 + 9)(12 + 1) = x^3 + (7 - x)^3##
The Attempt at a Solution
I used the last equation (the one with x in it) and equated it to 1729 to solve for ##x##. But I need to solve the question without a calculator, and I need to use the information given in the question, which I did not.
I noticed that the 3rd form equation ## 1729 = 7(10 + 9)(12 + 1)## contains the same terms as those in the cubes, ##(12 + 1)## for ##(12^3 + 1^3)## and ##(10 + 9)## for ##(10^3 + 9^3)##. I think this is important, but I have no idea of how to use this information.
Thank you for helping