In the book, Lewis Carroll in Numberland, the author mentions that one of the problems that Lewis Carroll encountered at Oxford in 1854
was to solve the following equations:
x3 - y3 = 98
x - y = 2
Can you solve for x and y? Show all work.
Solution to the Problem:
There are two answers: (5, 3) and (-3, -5).
Since x = y + 2 (from the second equation), substitute for x in the first equation:
(y + 2)3 - y3 = 98
y3 + 6y2 + 12y + 8 - y3 = 98
6y2 + 12y - 90 = 0
y2 + 2y - 15 = 0
(y - 3) (y + 5) = 0
y = 3, -5
So, the answers are (5, 3) and (-3, -5).