Ok so you are given; a, b, c are integers
abc = 729
and a + b + c = 91
Find a^2 + b^2 + c^2
How could I do this algebraically?
Say $\displaystyle c = 1$. Therefore, we have :
$\displaystyle ab = 729$
$\displaystyle a + b = 90$
Substitute :
$\displaystyle a(90 - a) = 729$
$\displaystyle 90a - a^2 = 729$
$\displaystyle a^2 - 90a + 729 = 0$
Solve for $\displaystyle a$.
Facts for the lazy :
Spoiler:
And for the curious :
Spoiler:
Finding the sum of the squares shouldn't be too hard now (remember $\displaystyle c = 1$)