Thread: Tricky Problem

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?

Hint: 1+9+81=91

Say . Therefore, we have :




Substitute :





Solve for .

Facts for the lazy :

Spoiler:

You sure ?

Spoiler:

And for the curious :

Spoiler:

Since you would get a polynomial with the same coefficients if you had substituted instead of , the two solutions of the quadratic equation are and .
Oh, and by the way, you just factored 729 into smaller factors

Finding the sum of the squares shouldn't be too hard now (remember )