1 Answer | Add Yours
All the sets of positive integers (a, b, c) have to be determined such that `1/a + 1/b + 1/c = 1` .
To solve this problem start with the general assumption `a<=b<=c` .
The minimum value that a can take on is 2; if a = 1, `1/b + 1/c` would have to be equal to zero which is not possible.
For a = 2, `1/b + 1/c = 1/2` . This is possible only when b has a value greater than 2 else 1/c would have to be equal to 0. For b = 3, c = 6 and for b = 4, c = 4. If b > 4, c is less than than b.
For a = 3; b = 3 and c = 3
a cannot take on any larger values as that would make it greater than b. There is a finite set of values of the variables a, b and c that satisfies the given equation.
The solution set (a, b, c) is (2, 3, 6), (2, 4, 4) and (3, 3, 3).
We’ve answered 319,809 questions. We can answer yours, too.Ask a question