If a,b and c are integers such that a+b+c=91 and abc=729,
determine the value of a^2 + b^2 + c^2
We first need to find factors of 729, such that they add
up to 91. The only ones that work are 81, 9 and 1 (yes,
1 can be a factor, even though it is usually not considered.)
81 * 9 * 1 = 729
81 + 9 + 1 = 91
That takes us to 81^2 + 9^2 + 1^2
x = 81^2 + 9^2 + 1^2
x = 6561 + 81 + 1
x = 6643
a = 81
b = 9
c = 1